We propose a novel string theory propagating in a non-commutative deformation of the four dimensional space T* T^2 whose scattering states correspond to superconformal theories in 5 dimensions and the scattering amplitudes compute superconformal indices of the corresponding 5d theories. The superconformal theories are obtained by M-theory compactifications on singular CY 3-folds or equivalently from a web of 5-branes of type IIB strings. The cubic interaction of this string theory for primitive winding modes corresponds to the (refined) topological vertex. The oscillator modes of the string theory correspond to off-shell states and carry information about co-dimension 2 defects of the superconformal theory. Particular limits of a subset of scattering amplitudes of this string theory lead to the partition functions of A_n Gaiotto theories for all n, compactified on S^4, i.e., to amplitudes of all Toda theories.
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric partition function of two-dimensional supersymmetric theories on a torus i.e. of the elliptic genus. The partition functions in question are on manifolds homeomorphic to the ones obtained by gluing solid tori. Such gluing involves the choice of a large diffeomorphism of the boundary torus, along with the choice of a large gauge transformation for the background…
We investigate asymmetric orbifold models constructed from non-supersymmetric heterotic strings. We systematically classify the asymmetric orbifold models with standard embeddings and present a list of asymmetric orbifolds which are geometrically interpreted as toroidal compactifications of non-supersymmetric heterotic strings. By studying non-standard embedding models, we also construct examples of the {\em supersymmetric} asymmetric orbifold models based on non-supersymmetric heterotic strings.
We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $Σ_g$. We compute the $\mathcal{M}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2 \times S^1$ with a topological twis…
We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any diffeomorphism-invariant scheme and in the presence of $G_F$ 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function has a non-holomorphic dependence on the flavor parameters. We show this explicitly for the 2d torus partition function, $Z_{T^2}$, and for a large class of 4d partition functions on half-BPS four-manifolds, $Z_{\mathcal{M}_4}$-…
We derived an existence criterion to the Supersymmetric String Theory with Torsion proposed by Strominger and proved the existence of such theory for a class of Calabi-Yau threefolds.
We search for the possibility to have supersymmetric string bits at finite discretization $J$. From a general setup we find that the string bits can be made supersymmetric modulo a single defect mode which is not expected to have any sensible effect in the continuum limit.
We study four-dimensional $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory with $2N$ fundamental hypermultiplets in the self-dual $Ω$-background. The partition function simplifies at special points of the parameter space and is related to the partition function of two-dimensional Yang-Mills theory on $S^{2}$. We also consider the insertion of a Wilson loop operator in two-dimensional Yang-Mills theory and find the corresponding operator in the four-dimensional $\mathcal{N}=2$ gauge theory.
We compare the logarithm of the degeneracy of BPS saturated elementary string states and the string modified Bekenstein-Hawking entropy of the corresponding black holes in N=2 supersymmetric heterotic string compactification to four dimensions. As in the case of N=4 supersymmetric theory, the two results match up to an overall undetermined numerical factor. We also show that this undetermined numerical constant is identical in the N=2 and N=4 supersymmetric theories, therby showing that the agreement between the Bekenstein-Hawking entropy and the microscopic entropy for N=2 theories does not r…
Recently Berkovits and Vafa have shown that the bosonic string can be viewed as the fermionic string propagating in a particular background. Such a background is described by a somewhat unusual $N=1$ superconformal system. By coupling it to $N=1$ supergravity I construct a local supersymmetric action for the bosonic string.
We discuss the supersymmetric formulation of the nonhermitian $β= 2$ random matrix partition function with one bosonic flavor. This partition function is regularized by adding one conjugate boson and fermion each. A supersymmetric nonlinear $σ$-model for the resulting Goldstone degrees of freedom is obtained using symmetry arguments only. For a Gaussian probability distribution the same results are derived using superbosonization and the complex orthogonal polynomial method. The symmetry arguments apply to any model with the same symmetries and a mass gap, and demonstrate the universality of t…
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov's partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model we …
We show that the bosonic string theory quantized in the Beltrami parametrization possesses a supersymmetric structure like the vector-supersymmetry already observed in topological field theories.
We calculate partition functions for supersymmetric heterotic theories on Melvin background with Wilson line. These functions coincide with partition functions for some of non-supersymmetric heterotic theories in appropriate limits. This suggests that non-supersymmetric heterotic theories are equivalent to supersymmetric theories on supersymmetry-breaking backgrounds, just as in the case of recently conjectured IIA-0A duality.
Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vorte…
We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $σ$-model conformal invariance conditions up to four-loop order.
We use supersymmetric localization to compute the partition function of N=2 super-Yang-Mills on S^4 in the presence of a gauged linear sigma model surface defect on a S^2 subspace. The result takes the form of a standard partition function on S^4, with a modified instanton partition function and an additional insertion corresponding to a shifted version of the gauged linear sigma model partition function.
In this note, we propose the free energy of general \emph{non-supersymmetric} black hole attractors arising in type IIA(B) superstrings on 3-fold Calabi-Yau, in the supergravity limit. This, by definition, differs from its counterpart BPS free energy by a factor of $4 $. Correspondingly, a mixed ensemble for these black holes is proposed.
Using the ambitwistor string, we complete the list of celestial OPE coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet CFT to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to…
T-dualities of the non-supersymmetric string models, which are constructed by twisted compactifications, are investigated. We show that the T-duality groups of such models are obtained by imposing congruence conditions on $O\left( d_{L},d_{R},\mathbb{Z}\right) $, that is, the non-supersymmetric string models are invariant under congruence subgroups of $O\left( d_{L},d_{R},\mathbb{Z}\right)$. We also point out that the transitions among the non-supersymmetric models can be induced by acting $O\left( d_{L},d_{R},\mathbb{Z}\right) $ transformations.
In this thesis we study the spectra of supersymmetric states in string theory compactifications with eight and sixteen supercharges, with special focus placed on the quantum states of black holes and the phenomenon of wall-crossing in these theories. A self-contained introduction to the relevant background material is included.
We construct the classical configurations of BPS states with 1/4 unbroken supersymmetries in four-dimensional N=4 SU(n+1) supersymmetric Yang-Mills theory, and discuss that these configurations correspond to string networks connecting (n+1) D3-branes in Type IIB string theory.
Anomalous U(1)s are omnipresent in realizations of the Standard Model using D-branes. Such models are typically non-supersymmetric, and the anomalous U(1) masses are potentially relevant for experiment. In this paper, the string calculation of anomalous U(1) masses (hep-th/0204153) is extended to non-supersymmetric orientifolds.
We construct BPS saturated regular configurations of N=4 SU(3) supersymmetric Yang-Mills theory carrying non-parallel electric and magnetic charges. These field theory BPS states correspond to the string theory BPS states of 3-string junctions connecting three different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes.
We consider non-supersymmetric four-dimensional closed string theories constructed out of tensor products of N=2 minimal models. Generically such theories have closed string tachyons, but these may be removed either by choosing a non-trivial partition function or a suitable Klein bottle projection. We find large numbers of examples of both types.
Non-Abelian strings are considered in {\em non}-supersymmetric theories with fermions in various appropriate representations of the gauge group U($N$). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases, we observe a non-trivial $N$ dependence.
We analyze non-supersymmetric four dimensional open string models of type IIB string theory compactified on $T^2\times K3$ with Scherk-Schwarz deformation acting on an $S^1$ of the $T^2$ torus. We find that there are always two solutions to the tadpole conditions that are shown to be connected via Wilson lines in an non-trivial way. These models although non-supersymmetric, are free of R-R and NS-NS tadpoles.
We give a pedagogical introduction to the study of supersymmetric partition functions of 3D $\mathcal{N}{=}2$ supersymmetric Chern-Simons-matter theories (with an $R$-symmetry) on half-BPS closed three-manifolds---including $S^3$, $S^2 \times S^1$, and any Seifert three-manifold. Three-dimensional gauge theories can flow to non-trivial fixed points in the infrared. In the presence of 3D $\mathcal{N}{=}2$ supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some mor…
We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with N=2-preserving superpotential, in which case the Abrikosov string is found to be 1/2-BPS saturated. Adding a quadratic small perturbation in the superpotential breaks N=2 supersymmetry to N=1 supersymmetry. Then the Abrikosov string is no longer BPS saturated. The difference between the string tensions for the non-BPS and BPS saturated situation is found to be negative to the first order of the perturbation parameter.
The previously proposed generalized action principle approach to supersymmetric extended objects is considered in some details for the case of heterotic string in $D=3, 4, 6 ~and~ 10$ space--time dimensions. The proof of the 'off--shell' superdiffeomorphism invariance of the generalized action is presented. The doubly supersymmetric geometric approach to heterotic string is constructed on the basis of generalized action principle (instead of the geometrodynamic condition, used for this previously). It is demonstrated that $D=3$ heterotic string is described by $n=(1,0)$ supersymmetric generali…
We discuss a rigid string model proposed by Casalbuoni and Longhi. Constraints for the massive states are solved to find the physical states and the mass spectrum. We also find its supersymmetric extension with the kappa symmetry. The supersymmetry transformations are found starting from on-shell transformations using the Dirac bracket.
Rotating IIB strings in AdS_5 x S^5 become ultra-relativistic, and hence effectively tensionless, in the limit of large angular momentum on S^5. We have shown previously that such tensionless strings may preserve supersymmetry. Here we extend this result to include a class of supersymmetric tensionless strings with arbitrary SO(6) angular momentum. We close with some general comments on tensionless strings in AdS_5 x S^5.
We consider the flat supersymmetric D2 and anti-D2 system, which follows from ordinary noncommutative D2 anti-D2 branes by turning on an appropriate worldvolume electric field describing dissolved fundamental strings. We study the strings stretched between D2 and anti-D2 branes and show explicitly that the would-be tachyonic states become massless. We compute the string spectrum and clarify the induced noncommutativity on the worldvolume. The results are compared with the matrix theory description of the worldvolume gauge theories.
In this short note we review the main features of open-string orbifolds with a quantised flux for the NS-NS antisymmetric tensor in the context of the open descendants of non-supersymmetric asymmetric orbifolds with a vanishing cosmological constant.
We study the different quantum phases that occur in massive ${\cal N}=2$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling $Λ/M$ is gradually increased from 0 to infinity. The phases can be identified by computing the exact partition function by saddle-points, combining supersymmetric localization and the Seiberg-Witten formalism. In all cases, we find two phases, a weak coupling and a strong coupling phase, separated by a critical point described by a superconformal field theory or involving superconformal sectors. In crossing the critical point, the dominant saddle-poi…
We study the new case of the application of the JKLMR conjecture on the connection between the exact partition functions of $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on $S^2$ and special Kähler geometry on the moduli spaces of Calabi-Yau manifold $Y$. The last ones arise as manifolds of the supersymmetric vacua of the GLSM. We establish this correspondence using the Mirror symmetry in Batyrev's approach. Namely, starting from the two-moduli non-Fermat Calabi-Yau manifold $X$ we construct the dual GLSM with the supersymmetric vacua $Y$, which is the mirror for $X$. Kn…
The first part of this thesis is a general introduction to the bosonic and fermionic string theory, to the concept of D brane and to string dualities. A discussion of anomalies cancellation closes the chapter. The second part of the thesis reviews the basics of orientifold and orbifold constructions and the Scherk-Schwarz mechanism of supersymmetry breaking. The last part starts with an introduction to standard cosmology and inflation. Alternatives to inflation inspired from string theory and time dependent orbifolds are discussed. Finally time dependent solutions of non-supersymmetric strings…
We present a detailed analysis of non-supersymmetric spacetime varying string vacua which can lead to an exponential hierarchy between the electroweak and the gravitational scales. In particular, we identify a limit in which these vacua can be interpreted as supersymmetric vacua of F-theory. Furthermore, we study the properties of these solutions as seen by $D7$-brane probes and establish a non-supersymmetric analogue of the enhancon mechanism.
A class of non-supersymmetric string backgrounds can be constructed using twists that involve space-time fermion parity. We propose a non-perturbative definition of string theory in these backgrounds via gauge theories with supersymmetry softly broken by twisted boundary conditions. The perturbative string spectrum is reproduced, and qualitative effects of the interactions are discussed. Along the way, we find an interesting mechanism for inflation. The end state of closed string tachyon condensation is a highly excited state in the gauge theory which, in all likelihood, does not have a geomet…
These notes are based on lectures given by C. Callan and J. Harvey at the 1991 Trieste Spring School on String Theory and Quantum Gravity. The subject is the construction of supersymmetric soliton solutions to superstring theory. A brief review of solitons and instantons in supersymmetric theories is presented. Yang-Mills instantons are then used to construct soliton solutions to heterotic string theory of various types. The structure of these solutions is discussed using low-energy field theory, sigma-model arguments, and in one case an exact construction of the underlying superconformal fiel…
We study non-supersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on Calabi-Yau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the non-supersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for non-supersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.
N=1, D=4 Superstring possessing $SO(6)\otimes SO(5)$ symmetry action and with the same gauge symmetry obtained from zero mass spectrum of vector meson as well, is constructed from the bosonic string in twenty six dimensions. Without breaking supersymmetry, the gauge symmetry of the model descends to the supersymmetric standard model of the electroweak scale in four dimension.It is proved that there can be three generations in the model
Extending our previous work on SU(3), we construct spherically symmetric BPS saturated regular configurations of N=4 SU(N) supersymmetric Yang-Mills theory preserving 1/4 supersymmetry, and investigate their features. We also give exact solutions in the case some of the free parameters of the general solutions take certain values. These field theory BPS states correspond to the string theory BPS states of multi-pronged strings connecting N different D3-branes by regarding the N=4 supersymmetric Yang-Mills theory as an effective field theory on parallel D3-branes. We compare our solutions with …
We study non-supersymmetric solutions of five dimensional N=2 supergravity theories coupled to an arbitrary number of abelian vector multiplets. The solutions constructed can be considered as deformations of known supersymmetric black hole and string solutions. General constraints coming from the analysis of the equations of motion are derived. These represent explicit conditions on the charges of the black holes and strings. The constraints are analyzed for theories where the scalar manifolds are symmetric spaces and explicit solutions are constructed in cases where the prepotential of the th…
We discuss tachyon-free examples of (Type IIB on) non-compact non-supersymmetric orbifolds. Tachyons are projected out by discrete torsion between orbifold twists, while supersymmetry is broken by a Scherk-Schwarz phase (+1/-1 when acting on space-time bosons/fermions) accompanying some even order twists. The absence of tachyons is encouraging for constructing non-supersymmetric D3-brane gauge theories with stable infrared fixed points. The D3-brane gauge theories in our orbifold backgrounds have chiral N = 1 supersymmetric spectra, but non-supersymmetric interactions.
The unitarity of the NS supersymmetric coset SL(2,R)/U(1) is studied for the discrete representations. The results are applied to the proof of the no-ghost theorem for fermionic strings in AdS(3) x N in the NS sector. A no-ghost theorem is proved for states in flowed discrete representations.
The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously due to the decay of these particles as the vacuum on the Coulomb branch is varied. We show that this decay process is well described by semi-classical field configurations purely in terms of the low energy effective action on the Coulomb branch even when it occurs at strong coupling. The resulting picture of the stable supersymmetric spectrum is a generalization of the ``string web'' picture of these states found in string constructions of certain theories.
We propose a twistor--like formulation of N=1, D=3,4,6 and 10 null superstrings. The model possesses N=1 target space supersymmetry and n=D-2 local worldsheet supersymmetry, the latter replaces the kappa-symmetry of the conventional approach to the strings. Adding a Wess--Zumino term to a null superstring action we observe a string tension generation mechanism: the induced worldsheet metric becomes non-degenerate and the resulting model turns out to be classically equivalent to the heterotic string.
The massless spectrum of the ten dimensional USp(32) type I string has an N=1 supergravity multiplet coupled to non-supersymmetric matter. This raises the question of the consistency of the gravitino interactions. We resolve this apparent puzzle by arguing for the existence of a local supersymmetry which is non-linearly realised in the open sector. We determine the leading order low energy effective Lagrangian. Similar results are expected to apply to lower dimensional type I models where supergravity is coupled to non-supersymmetric branes.
Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($β\rightarrow{0}$) behavior of supersymmetric partition functions $Z^{SUSY}(β)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\ln Z^{SUSY}(β)$ terminates at order $β^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in th…
We review the construction of non-supersymmetric open string vacua in various dimensions. They can be obtained either projecting the (compactified) non-supersymmetric 0B theory, or applying the Scherk-Schwarz mechanism to open strings. Generically, these vacua generate a non-vanishing cosmological constant. However, one can construct particular kinds of Scherk-Schwarz compactifications with vanishing cosmological constant, at least for low orders, based on asymmetric orbifolds. A generic feature of these models is that supersymmetry remains unbroken on the branes at all mass level, while it is…
We study closed string tachyon condensation on general non-supersymmetric orbifolds of C^2. Extending previous analyses on Abelian cases, we present the classification of quotients by discrete finite subgroups of GL(2; C) as well as the generalised Hirzebruch-Jung continued fractions associated with the resolution data. Furthermore, we discuss the intimate connexions with certain generalised versions of the McKay Correspondence.
We construct the basic Neveu-Schwarz (NS) brane solutions of non-relativistic string theory using longitudinal T-duality as a solution generating technique. Extending the NS background fields to a supergravity multiplet, we verify that all solutions we find are half-supersymmetric. The two perturbative solutions we find both have an interpretation as the background geometry outside a string-like object. Correspondingly, we refer to these non-Lorentzian backgrounds as winding string and unwound string solution. Whereas the winding string is part of the on-shell spectrum of non-relativistic stri…
We present plane-wave-type solutions of the lowest order superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a stringy generalization of the Brinkmann metric. Some conspiracy between the metric and the axion field is required. We show that there exists a special class of these solutions, for which $α^\prime$ stringy corrections to the effective on-shell action, to the equations of motion (and therefore to the solutions themselves), and to the supersymmetry transformations vanish. We call these solutions supersymmetric st…
In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional $N=2$ supersymmetry and we find multiple $N=2$, $d=1$ supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with …
