We analyze the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be cancelled out by choosing the boundary condition of the string appropriately. Our results, together with the recent result of arXiv:0807.5127, where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analysed, allow us to conclude that Legendre transform is at best capable of cancelling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancellation of the leading linear divergences generally and find that many well-known supergravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N=1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be cancelled away with the Legendre transform. Finally we end with some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.
Duality Symmetry is studied for heterotic string orbifold compactifications in the presence of a general background which in addition to the metric and antisymmetric tensor contains both discrete and continuous Wilson lines background.
We summarise the status of an intriguing new duality between planar maximally helicity violating scattering amplitudes and light-like Wilson loops in N=4 super Yang-Mills. In particular, we focus on the role played by (dual) conformal symmetry, which is made predictive by deriving anomalous conformal Ward identities for the Wilson loops. Assuming the duality, the conformal symmetry of the dual Wilson loops becomes an unexpected new symmetry of scattering amplitudes in N=4 SYM.
We discuss the cyclic Wilson loop, i.e. a rectangular Wilson loop that spans the entire compactified time axis in the imaginary time formalism. The result of a perturbative calculation at $O(α_s^2)$ is given, with the main focus on the ultraviolet divergences of this operator. Based on a general analysis of divergences in loop diagrams, we find that, unlike usual Wilson loops, the cyclic loop does not have cusp divergences but intersection divergences, where the intersections arise due to the periodic boundary conditions. As a result, the cyclic Wilson loop itself is not multiplicatively renor…
We discuss the origin of the Wilson polygon - MHV amplitude duality at the perturbative level. It is shown that the duality for the MHV amplitudes at one-loop level can be proven upon the peculiar change of variables in Feynman parametrization and the use of the relation between Feynman integrals at the different space-time dimensions. Some generalization of the duality which implies the insertion of the particular vertex operator at the Wilson triangle is found for the 3-point function. We discuss analytical structure of Wilson loop diagrams and present the corresponding Landau equations. The…
We study Wilson loops in the 4-dimensional N=2 supersymmetric quiver/M theory duality recently constructed by Gaiotto and Maldacena, that is conjectured to be dual to M2 branes on AdS_5\times S^4 fibered over Σ_2. We use the localization method raised by Pestun, in order to compute the Wilson loop in 4-dimensional N=2 supersymmetric linear quiver gauge theory. We obtained the consistent results in the quiver gauge theory and the 11-dimensional supergravity. This match supports the N=2 quiver SCFT / M theory supergravity duality.
We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fix…
We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.
The Wilson loop in N=4 supersymmetric Yang-Mills theory admits a dual description as a macroscopic string configuration in the adS/CFT correspondence. We discuss the correction to the quark anti-quark potential arising from the fluctuations of the superstring.
We find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the 1/2 BPS Wilson loops from known results of the partition function. These relations are interpreted as an open-closed duality where the closed string background is shifted by the insertion of Wilson loops due to a back-reaction. Using the connection between ABJ theory and the topological string on local P1 x P1, we explicitly write down non-trivial relations between open and closed string amplitudes.
We discuss formulation of Wilson polygon - MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the dimensional regularization and the off-shell one. We suggest new interpretation of all types of box diagrams in terms of the dual simplex in dimensional regularization and describe its degeneration to the Wilson polygon. The interesting nullification phenomena for the low-energy amplitudes in the Higgsed phase has been found.
An intriguing new duality between planar MHV gluon amplitudes and light-like Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks of the duality by performing a two-loop calculation of the rectangular and pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal Ward identity for the Wilson loops and analyse its consequences. Starting from six points, the Ward identity allows for an arbitrary function of conformal invariants to appear in the expression for the Wilson loop. We compute this function at six points and two loops and discuss its implica…
We study the action of S-duality on half-BPS Wilson loop operators in 5d $\mathcal{N}=1$ theories. The duality is the statement that different massive deformations of a single 5d SCFT are described by different gauge theories, or equivalently that the SCFT points in parameter space of two gauge theories coincide. The pairs of dual theories that we study are realized by brane webs in type IIB string theory that are S-dual to each other. We focus on $SU(2)$ SQCD theories with $N_f \le 4$ flavors, which are self-dual, and on $SU(3)$ SQCD theories, which are dual to $SU(2)^2$ quiver theories. From…
We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ spacetime, which corresponds to 4D $\mathcal{N}=4$ non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual $AdS_5\times S_5$ but with the constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop)…
We study the algebra of BPS Wilson loops in 3d gauge theories with N=2 supersymmetry and Chern-Simons terms. We argue that new relations appear on the quantum level, and that in many cases this makes the algebra finite-dimensional. We use our results to propose the mapping of Wilson loops under Seiberg-like dualities and verify that the proposed map agrees with the exact results for expectation values of circular Wilson loops. In some cases we also relate the algebra of Wilson loops to the equivariant quantum K-ring of certain quasi projective varieties. This generalizes the connection between…
We study the first non-planar correction to gluon scattering amplitudes in ${\cal N}=4$ SYM theory. The correction takes the form of a double trace partial amplitude and is suppressed by one power of $1/N$ with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality relates the amplitude to the correlation function of two infinite null polygonal Wilson lines that are subject to a quantum periodicity constraint. We test the duality perturbatively at one-loop order …
We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $\mathcal{N}\ge 4$ supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator…
We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain "loop integrand" defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-…
We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.
One of the many remarkable features of MHV scattering amplitudes is their conjectured equality to lightlike polygon Wilson loops, which apparently holds at all orders in perturbation theory as well as non-perturbatively. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the IR and UV divergences from amplitudes and Wilson loops respectively. In this paper we demonstrate, by explicit calculation, the completely unanticipated fact that the equality continues to hold at two loops through order epsilon in dimensional regularizat…
We classify bosonic $\mathcal{N}=(2,2)$ supersymmetric Wilson loops on arbitrary backgrounds with vector-like R-symmetry. These can be defined on any smooth contour and come in two forms which are universal across all backgrounds. We show that these Wilson loops, thanks to their cohomological properties, are all invariant under smooth deformations of their contour. At genus zero they can always be mapped to local operators and computed exactly with supersymmetric localisation. Finally, we find the precise map, under two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilso…
In this lecture, I put forward conjectures asserting that, in all noncommutative field theories, (1) open Wilson lines and their descendants constitute a complete set of interpolating operators of `noncommutative dipoles', obeying dipole relation, (2) infrared dynamics of the noncommutative dipoles is dual to ultraviolet dynamics of the elementary noncommutative fields, and (3) open string field theory is a sort of noncommutative field theory, whose open Wilson lines are interpolating operators for closed strings. I substantiate these conjectures by various intuitive arguments and explicit com…
We study supersymmetric Wilson loops in the ${\cal N} = 6$ supersymmetric $U(N_1)_k\times U(N_2)_{-k}$ Chern-Simons-matter (CSM) theory, the ABJ theory, at finite $N_1$, $N_2$ and $k$. This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the $U(N_1) \times U(N_2)$ lens space matrix model exactly, we perform an analytic continuation, $N_2$ to $-N_2$, to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and only valid in perturbation theory. Via a Sommerfeld-Watson type transform, we provide a nonperturbative com…
We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call ``fermionic T-duality''. This is a non-local redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. This duality maps a supersymmetric background to another supersymmetric background with different RR fields and a different dilaton. We show that a certain combination of bosonic and fermionic T-dualities maps the full superstring theory on $AdS_5 \times S^5$ back to itself in such a way that gluon…
We compute the four-point amplitude with external adjoint particles in $\mathcal{N}=2$ SCQCD at two loops using $\mathcal{N}=1$ superspace Feynman diagrams, extending the results of arXiv:1406.7283. We consider the diagrammatic difference with the corresponding process of $\mathcal{N}=4$ SYM finding a non vanishing result, which is a non trivial function of the kinematic variables. This demonstrates that in $\mathcal{N}=2$ SCQCD, even in the sector with external particles in the vector multiplet, the amplitude/Wilson loop duality is inevitably broken at two loops.
We study the M(atrix) theory which describes the $E_8 \times E_8$ heterotic string compactified on $S^1$, or equivalently M-theory compactified on an orbifold $(S^1/\integer_2) \times S^1$, in the presence of a Wilson line. We formulate the corresponding M(atrix) gauge theory, which lives on a dual orbifold $S^1 \times (S^1 / \integer_2)$. Thirty-two real chiral fermions must be introduced to cancel gauge anomalies. In the absence of an $E_8 \times E_8$ Wilson line, these fermions are symmetrically localized on the orbifold boundaries. Turning on the Wilson line moves these fermions into the i…
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in te…
We propose an SL(2,R) Chern-Simons description of Liouville field theory (LFT), whose correlation function duals to partition function of N=2 SU(2) gauge theories. We give the dual expressions for conformal blocks, fusion rules, and Wilson loop operators in Chern-Simons theory. By realizing Wilson loop operator in Liouville as a Hopf link in S^3 on which lives an SL(2,R) Chern-Simons theory, we obtain an alternative description of monodromy of this loop operator in Liouville field theory as the ratio of link invariants. We show how to calculate t'Hooft loops in the simplest example -- the N=4 …
We present the coset structure of the untwisted moduli space of heterotic $(0,2) \; Z_N$ orbifold compactifications with continuous Wilson lines. For the cases where the internal 6-torus $T_6$ is given by the direct sum $T_4 \oplus T_2$, we explicitly construct the Kähler potentials associated with the underlying 2-torus $T_2$. We then discuss the transformation properties of these Kähler potentials under target space modular symmetries. For the case where the $Z_N$ twist possesses eigenvalues of $-1$, we find that holomorphic terms occur in the Kähler potential describing the mixing of comple…
By using the gauge/gravity duality and the Maldacena prescription we compute the expectation values of the Wilson loops in noncommutative Yang-Mills (NCYM) theory in (3+1) dimensions. We consider both the time-like and the light-like Wilson loops. The gravity dual background is given by a particular decoupling limit of (D1,D3) bound state of type IIB string theory. We obtain the velocity dependent quark-antiquark potential and numerically study how the dipole length and the potential change with velocity (for 0 < v < 1, i.e., the Wilson loop is time-like) of the dipole as well as noncommutativ…
We present how to construct elliptically fibered K3 surfaces via Weierstrass models which can be parametrized in terms of Wilson lines in the dual heterotic string theory. We work with a subset of reflexive polyhedras that admit two fibers whose moduli spaces contain the ones of the $E_{8}\times E_{8}$ or $\frac{Spin(32)}{\mathbb{Z}_{2}}$ heterotic theory compactified on a two torus without Wilson lines. One can then interpret the additional moduli as a particular Wilson line content in the heterotic strings. A convenient way to find such polytopes is to use graphs of polytopes where links are…
We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-'t Hooft operators, since in the purely electric case they reduce to the well-known Wilson loops, while in general they may carry 't Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on AdS^2\times S^2. We show that Wilson-'t Hooft operators are classifed by a pair of weights (electric and…
We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and factorization of power divergences for certain linear combinations of associated loop functions.
We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in ${\cal N}$=4 SYM to large-N (or quenched) QCD. We show that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Veneziano behavior of scattering amplitudes at high energies and fixed momentum transfer, when quark mass is small and/or the number of particles is large. We elaborate on this duality for string theory in a flat space, identifying the asymptotes of the disk amplitude and the Wilson loop of large-N QCD.
We test the renormalization of Wilson operators and the Mandelstam- Leibbrandt gauge in the case when the sides of the loop are parallel to the n, n* vectors used in the M-L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M-L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M-L gauge for loops containing spacelike lines.
We consider circular non-BPS Maldacena-Wilson loops in five-dimensional supersymmetric Yang-Mills theory (d = 5 SYM) both as macroscopic strings in the D4-brane geometry and directly in gauge theory. We find that in the Dp-brane geometries for increasing p, p = 4 is the last value for which the radius of the string worldsheet describing the Wilson loop is independent of the UV cut-off. It is also the last value for which the area of the worldsheet can be (at least partially) regularized by the standard Legendre transformation. The asymptotics of the string worldsheet allow the remaining diverg…
In this paper, minimal surface in $q$-deformed $AdS_5\times S^5$ with boundary a cusp is studied in detail. This minimal surface is dual to cusped Wilson loop in the dual field theory. We found that the area of the minimal surface has both logarithmic squared divergence and logarithmic divergence. The logarithmic squared divergence can not be removed by either Legendre transformation or the usual geometric substraction. We further make analytic continuation to the Minkowski signature %for the case without the jump and take the limit such that the two edges of the cusp become light-like and ext…
We study S-duality in N=4 super Yang-Mills with an arbitrary gauge group by determining the operator product expansion of the circular BPS Wilson and 't Hooft loop operators. The coefficients in the expansion of an 't Hooft loop operator for chiral primary operators and the stress-energy tensor are calculated in perturbation theory using the quantum path-integral definition of the 't Hooft operator recently proposed. The corresponding operator product coefficients for the dual Wilson loop operator are determined in the strong coupling expansion. The results for the 't Hooft operator in the wea…
We use the AdS/SYM correspondence to study the relevant effects of compactified dimensions on the D-brane dynamics. We present a detailed picture of the T-duality transition between branes in type IIA and type IIB supergravity. An analysis of the renormalization scheme coming from the expectation values of background fields and the role of Wilson lines in it is given. We finally explore finite size effects and T-duality maps on the description of Wilson loops by supergravity.
We discuss the analyticity properties of the Wilson--loop correlation functions relevant to the problem of soft high-energy scattering, directly at the level of the functional integral, in a genuinely nonperturbative way.
After pointing out the role of the compactification lattice for spectrum calculations in orbifold models, I discuss modular discrete symmetry groups for $Z_N$ or\-bi\-folds. I consider the $Z_7$ orbifold as a nontrivial example of a (2,2) model and give the generators of the modular group for this case, which does not contain $[SL(2,{\bf Z})]^3$ as had been speculated. I also discuss how to treat cases where quantized Wilson lines are present. I consider in detail an example, demonstrating that quantized Wilson lines affect the modular group in a nontrivial manner. In particular, I show that i…
Target space duality symmetries, which acts on Kähler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets $SU(n,1)\over SU(n)\times U(1)$ are $special$ Kähler, a fact which is exploited in deriving the extension of tree level duality transformation to include higher orders of the twisted moduli. Also, restrictions on these higher order terms are derived.
We test gauge/string duality by evaluating expectation values of small Wilson loops in pure Yang-Mills theories. On the gauge-theory side, there exists rich phenomenology. The dual formulation provides with a universal language to evaluate the gluon condensate and quadratic correction in terms of the metric in the fifth coordinate. Quantitatively, the estimated value of the gluon condensate is approximately 0.010 GeV^4.
We discuss gluon scattering amplitudes/null-polygonal Wilson loops of N = 4 super Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. We focus on the amplitudes/Wilson loops corresponding to the minimal surfaces in AdS_3, which are described by the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model. Using conformal perturbation theory and an interesting relation between the g-function (boundary entropy) and the T-function, we derive analytic expansions around the limit where the Wilson loops become regular-polygonal. W…
We apply the $δ$-expansion to the Gross-Neveu model in the large $N$ limit with Wilson fermion and investigate dynamical mass generation from inverse-mass expansion. The dimensionless mass $M$ defined via the effective potential is employed as the expansion parameter of the bare coupling constant $β$ which is partially renormalized by the subtraction of linear divergence. We show that $δ$-expansion of the $1/M$ series of $β$ is compatible with the mass renormalization. After the confirmation of the continuum scaling of the bare coupling without fermion doubling, we attempt to estimate dynamica…
As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal light-like Wilson loop at two loops in N=4 super Yang-Mills theory. We compare its finite part to the Bern-Dixon-Smirnov (BDS) conjecture for the finite part of the six-gluon amplitude. We find that the two expressions have the same behavior in the collinear limit, but they differ by a non-trivial function of the three (dual) conformally invariant variables. This implies that either the BDS conjecture or the gluon amplitude/Wilson loop duality fails for the six-gluon amplitude, starting from two loops. O…
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find that specific UV divergences arise from diagrams involving two cusps, implying the loss of finiteness and topological invariance at two-loop order. Studying those UV divergences we derive anomalous conformal Ward identities for n-cusped Wilson loops which restrict the finite part of the latter to conformally invariant functions. We also compute the four-cusp Wi…
We study the divergences of Wilson loops for a contour with a cusp of zero opening angle, combined with a nonzero discontinuity of its curvature. The analysis is performed in lowest order, both for weak and strong coupling. Such a spike contributes a leading divergent term proportional to the inverse of the square root of the cutoff times the jump of the curvature. As nextleading term appears a logarithmic one in the supersymmetric case, but it is absent in QCD. The strong coupling result, obtained from minimal surfaces in AdS via holography, can be used also for applications to entanglement e…
Planar gluon amplitudes in N=4 SYM are remarkably similar to expectation values of Wilson loops made of light-like segments. We argue that the latter can be determined by making use of the conformal symmetry of the gauge theory, broken by cusp anomalies. We derive the corresponding anomalous conformal Ward identities valid to all loops and show that they uniquely fix the form of the finite part of a Wilson loop with n cusps (up to an additive constant) for n=4 and n=5 and reduce the freedom in it to a function of conformal invariants for n>=6. We also present an explicit two-loop calculation f…
We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank $16$. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3 surfaces and express their parameters in terms of modular forms generalizing Siegel modular forms. In this way, we find a complete list of all dual non-geometric compactifications obtained by the …
There is growing evidence that on-shell gluon scattering amplitudes in planar N=4 SYM theory are equivalent to Wilson loops evaluated over contours consisting of straight, light-like segments defined by the momenta of the external gluons. This equivalence was first suggested at strong coupling using the AdS/CFT correspondence and has since been verified at weak coupling to one loop in perturbation theory. Here we perform an explicit two-loop calculation of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate that the relation holds beyond one loop. We also propose an ano…
We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the correct infrared behaviour, the Wilsonian effective action has to include certain ''closed string`` modes with prescribed couplings. In the case of quiver gauge theories, realized in string theory on orbifolds, we identify the required modes with a set of twisted sector fields. These closed string modes have exactly the prescribed couplings to correct the Wilsonia…
The BPS spectrum of type I' string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I', and it is demonstrated that the relevant states in type I' preserve supersymmetry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the D0-D8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I', and on the predic…
We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological B-model on C whose target is the moduli space MV of nonabelian vortex equations on Sigma. The N=2 S-duality conjecture implies that the duality group acts by autoequivalences on the derived category of MV. This statement can be regarded as an N=2 counterpart of the geometric Langlands duality…
The locally BPS Wilson loop and the pure gauge Wilson loop map under AdS/CFT duality to string world-sheet boundaries with standard and alternate quantizations of the world-sheet fields. This implies an RG flow between the two operators, which we verify at weak coupling. Many additional loop operators exist at strong coupling, with a rich pattern of RG flows.
We show that $U(N)$ $3d$ $\mathcal{N}=4$ supersymmetric gauge theories on $S^{3}$ with $N_{f}$ massive fundamental hypermultiplets and with a Fayet-Iliopoulos (FI) term are solvable in terms of generalized Selberg integrals. Finite $N$ expressions for the partition function and Wilson loop in arbitrary representations are given. We obtain explicit analytical expressions for Wilson loops with symmetric, antisymmetric, rectangular and hook representations, in terms of Gamma functions of complex argument. The free energy for orthogonal and symplectic gauge group is also given. The asymptotic expa…
The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R^4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L \ge 2 loops wou…
We examine several aspects of S-duality of four-dimensional noncommutative gauge theory. By making duality transformation explicit, we find that S-dual of noncommutative gauge theory is defined in terms of dual noncommutative deformation. In `magnetic' noncommutative U(1) gauge theory, we show that, in addition to gauge bosons, open D-strings constitute important low-energy excitations: noncritical open D-strings. Upon S-duality, they are mapped to noncritical open F-strings. We propose that, in dual `electric' noncommutative U(1) gauge theory, the latters are identified with gauge-invariant, …
We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a …
