We compute the 2-loop thermal partition function of Yang-Mills theory on a small 3-sphere, in the large N limit with weak 't Hooft coupling. We include N_s scalars and N_f chiral fermions in the adjoint representation of the gauge group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming only commutator interactions. From this computation one can extract information on the perturbative corrections to the spectrum of the theory, and the correction to its Hagedorn temperature. Furthermore, the computation of the 2-loop partition function is a necessary step towards determining the order of the deconfinement phase transition at weak coupling, for which a 3-loop computation is needed.
We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Omega-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlss…
We explore the dynamics of three-dimensional Chern-Simons gauge theories with N=2 supersymmetry and matter in the fundamental and adjoint representations of the gauge group. Realizing the gauge theories of interest in a setup of threebranes and fivebranes in type IIB string theory we argue for a Seiberg duality that relates Chern-Simons theories with non-trivial superpotentials.
We study Aharony dualities for 3d N=2 gauge theories of classical gauge group with one adjoint and fundamental matters. We work out the 3d superconformal index for the dual pairs to find the perfect matchings. Along with it, we enumerate the independent monopole operators parametrizing the Coulomb branches and confirm the nonperturbative truncation of the chiral rings, consistent with the proposed dualities.
We discuss electric-magnetic duality in two new classes of supersymmetric Yang-Mills theories. The models have gauge group $Sp(2\nc)$ or $SO(\nc)$ with matter in both the adjoint and defining representations. By perturbing these theories with various superpotentials, we find a variety of new infrared fixed points with dual descriptions. This work is complementary to that of Kutasov and Schwimmer on $SU(\nc)$ and of Intriligator on other models involving $Sp(2\nc)$ and $SO(\nc)$.
The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an arbitrary number of adjoint matters is determined. Analytic continuation of the 't Hooft coupling t is analyzed. The eigenvalue distribution turns out to be confined in a finite region even for a large t. The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.
We consider a dimensional reduction of 3+1 dimensional SU(N) Yang-Mills theory coupled to adjoint fermions to obtain a class of 1+1 dimensional matrix field theories. We derive the quantized light-cone Hamiltonian in the light-cone gauge A_- = 0 and large-N limit, and then solve for the masses, wavefunctions and structure functions of the color singlet ``meson-like'' and ``baryon-like'' boundstates. Among the states we study are many massless string-like states that can be solved for exactly.
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this reduction. We translate the identity between indices of the dual 4d theories to 3d. This produces various new identities between partition functions of 3d dual phases.
We study low-energy effective superpotentials for the phase with a confined photon in N=1 supersymmetric gauge theories with an adjoint matter $Φ$ and fundamental flavors $Q, \tilde Q$. Arbitrary classical gauge groups are considered. The results are used to derive the hyperelliptic curves which describe the Coulomb phase of N=2 supersymmetric QCD with classical gauge groups. These curves are in agreement with those proposed earlier by several authors. Our results also produce the curves relevant to describe the Coulomb phase of N=1 theories with a superpotential of the form $\tilde{Q} Φ^{l} Q…
We extend Gopakumar's prescription for constructing closed string worldsheets from free field theory diagrams with adjoint matter to open and closed string worldsheets arising from free field theories with fundamental matter. We describe the extension of the gluing mechanism and the electrical circuit analogy to fundamental matter. We discuss the generalization of the existence and uniqueness theorem of Strebel differentials to open Riemann surfaces. Two examples are computed of correlators containing fundamental matter, and the resulting worldsheet OPE's are computed. Generic properties of Go…
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-tw…
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partitio…
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 explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincaré duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoi…
We consider supersymmetric Sp(2N) gauge theories with F matter fields in the defining representation, one matter field in the adjoint representation, and no superpotential. We construct a sequence of dual descriptions of this theory using the dualities of Seiberg combined with the ``deconfinement'' method introduced by Berkooz. Our duals hint at a new non-perturbative phenomenon that seems to be taking place at asymptotically low energies in these theories: for small F some of the degrees of freedom form massless, non-interacting bound states while the theory remains in an interacting non-Abel…
In this paper we study dualities for $\mathcal{N}=2$ gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from $\mathcal{N}=4$ mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry $U(2)$ or $SU(2)$. We find that $SU(2)$ adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. A…
We study Seiberg-like dualities for 3d N=2 theories with flavors in fundamental and adjoint representations. The recent results of Intriligator and Seiberg provide a derivation of an Aharony duality from a Giveon-Kutasov duality. We extend their result to the case of more general theories involving various masses for fundamental quarks and adjoint fields. By fine tuning the vev of a scalar field and using various identifications between gauge groups and their singlet duals, we derive several examples of Aharony dualities. For theories with an adjoint field, we discuss the connection between th…
We study the phase structure of N = 1 supersymmetric Sp(2N_c) gauge theories with 2N_f fundamentals, an adjoint, and vanishing superpotential. Using a-maximization, we derive analytic expressions for the values of N_f below which the first several gauge-invariant operators in the chiral ring violate the unitarity bound and become free fields. In doing so we are able to explicitly check previous conjectures about the behavior of this theory made by Luty, Schmaltz, and Terning. We then compare this to an analysis of the first two 'deconfined' dual descriptions based on the gauge groups Sp(2N_f+2…
In this paper we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general $Ω$-background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. Comparing our results with those recently obtained by Iqbal et. al., who used the refined topological vertex method,…
Dynamics of SU(N_c) Yang--Mills theories with N_f adjoint Weyl fermions is quite different from that of SU(N_c) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N_f) --> SO(N_f). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of N_f=2 had been considered previously. Here we discuss N_f >= 3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions (with mass O(N_c^0)) from the standpoint of the…
We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial dependence on theta (the noncommutativity parameter) and to a rich dynamics. In particular the mass spectrum of the noncommutative U(1) theory with adjoint matter is similar to that of ordinary (commutative) two-dimensional large-N SU(N) gauge theory with adjoint matter. The noncommutative version of the 't Hooft model receives a non-trivial contribution to the v…
We propose a non-perturbative solution of N=2 supersymmetric gauge theory in five dimensions compactified on circle of a radius $R$. We consider the cases of the pure gauge theory as well as the theories with matter in the fundamental and in the adjoint representations. The pure theory as well as the one with adjoint hypermultiplet give rise to the known relativistic integrable systems with ${1\over{R}}$ playing the rôle of the speed of light. The theory with adjoint hypermultiplet exhibits some interesting finiteness properties. Talk given at the III International Conference ``Conformal Field…
In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormaliza…
We study $N = 2$ 3-d theories with two adjoints and fundamental flavors along with D-type superpotential. For superpotential $W_{D_{n+2}} = \mathrm{Tr} \left(X^{n+1}+X Y^2\right)$ with $n$ odd, we propose the 3d dualities, which we motivate from the dimensional reduction of the related 4-d theory. We consider the factorization of the superconformal index and match precisely the vortex partition function of the dual pairs. In the language of the Higgs branch localization, the nonzero contribution of the vortex partition function comes from the discrete Higgs vacua of the massively deformed theo…
We study two dimensional $N=(4,4)$ supersymmetric gauge theories with various gauge groups and various hypermultiplets in the fundamental as well as bi-fundamental and adjoint representations. They have " mirror theories " which become equivalent to them at the strong coupling. The theory with one fundamental and one adjoint has a Higgs branch which is parametrized by the adjoint matter. We also consider theories which involve an orientifold plane. The brane realization of the Matrix theory formulation of NS 5-branes in Type II string theories is also considered.
In this paper we complete the derivations of finite volume partition functions for QCD using random matrix theories by calculating the effective low-energy partition function for three-dimensional QCD in the adjoint representation from a random matrix theory with the same global symmetries. As expected, this case corresponds to Dyson index $β=4$, that is, the Dirac operator can be written in terms of real quaternions. After discussing the issue of defining Majorana fermions in Euclidean space, the actual matrix model calculation turns out to be simple. We find that the symmetry breaking patter…
We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; henc…
We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly m…
In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.
Large N gauge theories with adjoint matter can be numerically studied using lattice techniques. Eguchi-Kawai reductions holds for this theory and one can reduce the lattice model to a single site. Hybrid Monte Carlo algorithm can be used to simulate this model. One can either perform an exact computation of the "fermionic force" or use pseudo fermions as part of the HMC algorithm. The former algorithm is slower than the latter but has the advantage that one can work with any real number for the fermion flavor. Some results using both algorithms will be presented.
Partition functions for M2-brane theories in various backgrounds are computed. We consider in particular configurations of membranes at orbifold singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane theory for some of these configurations has been recently constructed in terms of N=6 Chern-Simons theories. The detailed structure of the partition functions as well as their transformation rules under the R-symmetry are explicitly computed using the Plethystic Programme.
We discuss a general procedure to obtain 1/2 BPS partition functions for generic N=1 quiver gauge theories. These functions count the gauge invariant operators (bosonic and fermionic), charged under all the global symmetries (mesonic and baryonic), in the chiral ring of a given quiver gauge theory. In particular we discuss the inclusion of the spinor degrees of freedom in the partition functions.
We argue, that for a general class of nontrivial bosonic theories the path integral can be related to an equivariant generalization of conventional characteristic classes.
We map out and explore the zoo of possible 4d N=1 superconformal theories which are obtained as RG fixed points of N=1 SQCD with N_f fundamental and N_a adjoint matter representations. Using "a-maximization," we obtain exact operator dimensions at all RG fixed points and classify all relevant, Landau-Ginzburg type, adjoint superpotential deformations. Such deformations can be used to RG flow to new SCFTs, which are then similarly analyzed. Remarkably, the resulting 4d SCFT classification coincides with Arnold's ADE singularity classification. The exact superconformal R-charge and the central c…
We consider a bound state problem for a family of supersymmetric gauge theories with fundamental matter. These theories can be obtained by a dimensional reduction of supersymmetric QCD from three dimensions to 1+1 and subsequent truncation of some of the fields. We find that the models without adjoint scalar converge to well-defined continuum limits and calculate the resulting spectra of these theories. We also find the critical value of coupling at which an additional massless state is observed. By contrast, the models containing adjoint scalars, seem to have a continuous mass spectrum in the…
We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the partition function is related to the Ray-Singer torsion defined on flat vector bundles for all odd-dimensional manifolds, and is equal to unity for even dimensions.
The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classica…
In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge theories with mixed representation fields have been suggested to describe the fundamental interactions well beyond the electroweak unification scale, and they are also closely related to supersymmetric QCD. In addition, they are studied as deformations of theories with pure adjoint matter in the context of adiabatic continuity. We provide some first results for ba…
We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes …
Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit $\widetilde{p}^μ(\equiv θ^{μν}p_ν) \to 0$. The adjoint chiral fermion carries no anomaly in the non-planar sector in $D=4k (k=1,2,...,)$ dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing.
We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c = c(p,1) = 13-6(p+1/p), the ``border'' of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c = c(p,1) which is similar to the A-D-E classification of c = 1 models.
We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the $T_N$ theory. The theories may be realized by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realized in various Higgs branches of the $T_3$ theory. A particularly interesting example is the $E_8$ theory which can be obtained by Higgsing the $T_6$ theory. We explicitly compute the partition function of the $E_8$ theory and find t…
We study $N=2$ supersymmetric gauge theories on a large family of squashed 4-spheres preserving $SU(2)\times U(1)\subset SO(4)$ isometry and determine the conditions under which this background is supersymmetric. We then compute the partition function of the theories by using localization technique. The results indicate that for $N=2$ SUSY, including both vector-multiplets and hypermultiplets, the partition function is independent of the arbitrary squashing functions as well as of the other supergravity background fields.
We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet-Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. As applicat…
We compute the partition functions of $\mathcal{N} = 1$ gauge theories on $S^2 \times \mathbb{R}^2_\varepsilon$ using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of $S^2$ and at the origin of $\mathbb{R}^2_\varepsilon$. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the $\mathcal{N} = 1$ partition functions on the $Ω$-background, and show that the Nekrasov partition functions can be recovered from these building blocks.
We calculate the one-loop partition function for a massless arbitrary-spin field on quotients of a general dimensional AdS background using the results of arXiv:1103.3627. We use these results to compute the one-loop partition function for a Vasiliev theory in AdS_5. An interesting form of the answer, suggestive of a vacuum character of an enhanced symmetry algebra is obtained. We also observe a close connection between the partition function for this Vasiliev theory and the d-dimensional MacMahon function.
Recently Witten conjectured the existence of a family of "extremal" conformal field theories (ECFTs) of central charge c=24k, which are supposed to be dual to three-dimensional pure quantum gravity in AdS3. Assuming their existence, we determine explicitly the genus two partition functions of k=2 and k=3 ECFTs, using modular invariance and the behavior of the partition function in degenerating limits of the Riemann surface. The result passes highly nontrivial tests and in particular provides a piece of evidence for the existence of the k=3 ECFT. We also argue that the genus two partition funct…
Recursion relations for the sphere $4$-point and torus $1$-point ${\cal W}_3$ conformal blocks, generalizing Alexei Zamolodchikov's famous relation for the Virasoro conformal blocks are proposed. One of these relations is valid for any 4-point conformal block with two arbitrary and two special primaries with charge parameters proportional to the highest weight of the fundamental irrep of $SU(3)$. The other relation is designed for the torus conformal block with a special (in above mentioned sense) primary field insertion. AGT relation maps the sphere conformal block and the torus block to the …
We study the partition function ${\cal N}=1$ 5D $U(N)$ gauge theory with $g$ adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus $g$ Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.
Generalized Konishi anomaly relations in the chiral ring of N=1 supersymmetric gauge theories with unitary gauge group and chiral matter field in two-index tensor representations are derived. Contrary to previous investigations of related models we do not include matter multiplets in the adjoint representation. The corresponding curves turn out to be hyperelliptic. We also point out equivalences to models with orthogonal or symplectic gauge groups.
Linear recursion relations for the instanton corrections to the effective prepotential are derived for N=2 supersymmetric gauge theories with one hypermultiplet in the adjoint representation of SU(N) using the Calogero-Moser parameterization of the Seiberg-Witten spectral curves. S-duality properties of the Calogero-Moser parameterization and conjectures on the Seiberg-Witten spectral curves generalized to arbitrary simply laced classical gauge groups are also discussed.
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individual conformal field theory factors have been classified. We illustrate the use of these constraints for theories of the type $SU(2)_{K_A}\otimes SU(2)_{K_B}$, finding all consistent theories for $K_A,K_B$ odd. Second we show how known diagonal modular invariants can be us…
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An explicit computation of the partition functions shows that unitarity is recovered in particular regions of parameter space and that the effective dynamics is described in terms of fermionic interacting models. For the first family, this connection with fermionic models uncovers an exact duality which is conjectured to hold in the nonabelian case as well.
We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric Kähler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct equivariantly twisted theories. Then, using localization, we compute their supersymmetric partition functions. As expected, these receive contributions from a classical, a one-loop, and an instanton term. It turns out that the one-loop term is trivial and that the instanton contributions are localized at the fixed points of the $U(1)$. In fact the full partition funct…
We study the partition function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as $Z(N)=e^{A}C^{-1/3}\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many…
A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations among the structure constants of the theory. All of these relations are shown to be a consequence of the associativity of the OPE, as well as the modular covariance properties of the torus one-point functions. Using these techniques we prove that for the proposed extremal conformal field theories at c=24k a consistent genus two vacuum amplitude exists for all k…
Deformation of N=2 quiver gauge theories by adjoint masses leads to fixed manifolds of N=1 superconformal field theories. We elaborate on the role of the complex three-form flux in the IIB duals to these fixed point theories, primarily using field theory techniques. We study the moduli space at a fixed point and find that it is either the two (complex) dimensional ALE space or three-dimensional generalized conifold, depending on the type of three-form flux that is present. We describe the exactly marginal operators that parameterize the fixed manifolds and find the operators which preserve the…
