Abhijit Gadde, Leonardo Rastelli
We study spin chains for superconformal quiver gauge theories in the moduli space of N=2 orbifolds. Independent of integrability, which is generally broken, we use the centrally extended SU(2|2) symmetry of the magnons to fix their dispersion relations and two-body S-matrices, as functions of the exactly marginal couplings.
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We find the exact solution for a finite size Giant Magnon in the $SU(2)\times SU(2)$ sector of the string dual of the $\mathcal{N}=6$ superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each $SU(2)$. In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.
We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the superconformal algebra. The symmetry breaking caused by the non(anti)commutativity of the (super)spaces is naturally interpreted as the modification of their coproduct emerging from the corresponding twist element. The remaining unbroken symmetries are determined by the commutative properties of those symmetry generators possessing the twist element. We also comment on…
It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The central charges of the $N=2$ algebra for the two gauge choices are in general different. Further, it is argued that the physical states in the light cone gauge theory can be obtained from the Liouville theory by a field redefinition.
We examine the string dual of the recently constructed $\mathcal{N}=6$ superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the $SU(2)\times SU(2)$ sector. We find a sigma-model limit in which the resulting sigma-model is two Landau-Lifshitz models added together. We consider a Penrose limit for which we can approach the $SU(2)\times SU(2)$ sector. Finally, we find a new Giant Magnon solution in the $SU(2)\times SU(2)$ sector corresponding to one magnon in each $SU(2)$. We put these results together to find the full magnon disp…
We extend the N=4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C^2/Z_n)^2 orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.
We obtain the action for a curved superconformal abelian M5 brane with the background R-symmetry gauge field turned on. We then restrict ourselves to superconformal M5 brane on a sphere times flat Minkowski space. We choose R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5 brane actions on $M_{1,1} \times S^4$ and $M_{1,2} \times S^3$ where actions and all fields, including the background gauge field, are real. Dimensional reduction along time gives real 5d SYM actions with nonabelian gene…
We apply Zeilberger summation to derive a closed formula for the wrapping correction to one-impurity states in the su(2) sector of the beta-deformed N=4 SYM theory at beta=1/2. As an application depending heavily on the result, we compute the large volume expansion of the wrapping correction.
We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy manifolds. By considering automorphisms of this realisation, we identify stringy analogues of two mirror maps proposed by Braun and Del Zotto for these manifolds.
In this paper we find preliminary evidence that N=2 superconformal QCD, the SU(N_c) SYM theory with N_f= 2 N_c fundamental hypermultiplets, might be integrable in the large N Veneziano limit. We evaluate the one-loop dilation operator in the scalar sector of the N=2 superconformal quiver with SU(N_c) X SU(N_{\check c}) gauge group, for N_c = N_{\check c}. Both gauge couplings g and \check g are exactly marginal. This theory interpolates between the Z_2 orbifold of N=4 SYM, which corresponds to \check g=g, and N=2 superconformal QCD, which is obtained for \check g -> 0. The planar one-loop dila…
The N=4, d=4 Yang-Mills conformal supersymmetry exhibits a very simple sub-sector described by four differential operators. The invariance under this subalgebra is big enough to determine the N=4 theory. Some attempts are done to interpret these differential operators.
Worldsheet string theory compactified on exceptional holomony manifolds is revisited following arXiv:1809.06376, where aspects of the chiral symmetry were described for the case where the compact space is a 7-dimensional G$_2$-holonomy manifold constructed as a Twisted Connected Sum. We reinterpret this result and extend it to Extra Twisted Connected Sum G$_2$-manifolds, and to 8-dimensional Generalized Connected Sum Spin(7)-manifolds. Automorphisms of the latter construction lead us to conjecture new mirror maps.
We consider $\mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able…
We prove that the invariance of the N=2 superconformal quantum mechanics is controlled by subalgebras of a given twisted superalgebra made of 6 fermionic (nilpotent) generators and 6 bosonic generators (including a central charge). The superconformal quantum mechanics actions are invariant under this quite large twisted superalgebra. On the other hand, they are fully determined by a subalgebra with only 2 fermionic and 2 bosonic (the central charge and the ghost number) generators. The invariant actions are Q_i-exact (i=1,2,...,6), with a Q_{i'}-exact (i'\neq i) antecedent for all 6 fermionic …
We propose Lagrangian formulations of a three-particles translation invariant $N=4$ superconformal mechanics based on the standard and twisted $(1,4,3)$ supermultiplets. We show that in the appropriate set of coordinates, in which the bosonic kinetic terms for each of the two cases take conformally-flat forms, the corresponding models produce just similar physical systems with the flipped angular part of bosonic potential $U(x)\rightarrow 1/U(x)$. This flipping looks so simple only being written in the "angle" variable, while in the standard variables it looks more complicated to preserve the …
We study the integrability properties of planar N=2 superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of N=2 superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, …
We find an infinite family of $4D$ $\mathcal{N}=2$ interacting superconformal field theories which enter the description of the strong-coupling limit of $SU(2N+1)$ gauge theories with hypermultiplets in the $\wedge^2(\square)+\text{Sym}^2(\square)$ . These theories arise from the compactification of the $6D$ $(2,0)$ theory of type $A_{2N}$ on a sphere with two full twisted punctures and one minimal untwisted puncture. For $N=1$, this theory is the "new" rank-1 SCFT with $Δ(u)=3$ of Argyres and Wittig. Using the superconformal index, we finally pin down the properties of this theory.
We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate the superconformal index we quantize the field theory on S^3 X R and show that the twisted theory has an appropriate mass gap. This allows for the interactions to be switched off continuously without the superconformal index being changed. We test those techniques for theories which go through a non-trivial RG flow and for Seiberg dual theories. This leads to the conjecture of some group/number theo…
Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the $G/G$ coset theories. Their topological conformal algebra is generated by operators of dimensions $1$, $2$ and $3$ and can be regarded as an extension of the twisted $N=2$ superconformal algebra. These models possess an extended supersymmetry whose generators are exact in the topological BRST cohomology.
We study the two-dimensional topological abelian BF theory in the Lorenz gauge and, surprisingly, we find that the gauged-fixed theory is a free type B twisted N=(2,2) superconformal theory with odd linear target space, with the ghost field c being the pullback of the linear holomorphic coordinate on the target. The BRST operator of the gauge-fixed theory equals the total Q of type B twisted theory. This unexpected identification of two different theories opens a way for nontrivial deformations of both of these theories.
The parameter space of the Feigin-Fuks representations of the N=4 SU(2)$_k$ superconformal algebras is studied from the viewpoint of the specral flow. The $η$ phase of the spectral flow is nicely incorporated through twisted fermions and the spectral flow resulting from the inner automorphism of the N=4 superconformal algebras is explicitly shown to be operating as identiy relations among the generators. Conditions for the unitary representations are also investigated in our Feigin-Fuks parameter space.
We propose a general formula for the perturbative large N superconformal index of 5d quiver fixed point theories that have an AdS(6)xS(4)/Z(n) supergravity dual. This index is obtained from the parent theory by projecting to orbifold-invariant states and adding the twisted sector contributions. Our result agrees with expectations from the dual supergravity description. We test our formula against the direct computation of the index for Z(2) and Z(3) and find complete agreement.
We study $4D$ $\mathcal{N}=2$ superconformal field theories that arise as the compactification of the six-dimensional $(2,0)$ theory of type $E_6$ on a punctured Riemann surface in the presence of $\mathbb{Z}_2$ outer-automorphism twists. We explicitly carry out the classification of these theories in terms of three-punctured spheres and cylinders, and provide tables of properties of the $\mathbb{Z}_2$-twisted punctures. An expression is given for the superconformal index of a fixture with twisted punctures of type $E_6$, which we use to check our identifications. Several of our fixtures have …
We calculate the superconformal indices of recently discovered three-dimensional N=4,5 Chern-Simons-matter theories and compare them with the corresponding indices of supergravity on AdS4 times orbifolds of S7. We find perfect agreement in the large N and large k limit, provided that the twisted sector contributions at the fixed loci of the orbifolds are properly taken into account. We also discuss the index for the so-called "dual ABJM" proposal.
We study 4D N=2 superconformal theories that arise from the compactification of 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presence of punctures twisted by a Z_2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A_3, and provide tables of properties of twisted defects up through A_9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. As a…
Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from $\mathbb{Z}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for $|λ_I|<π^2$, where $λ_I$ are the 't Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly comput…
We consider a 2-dimensional conformal field theory (CFT) obtained from twisted compactification of the 4-dimensional N=4 super Yang-Mills theory on a Riemann surface with boundary. We find the boundary conditions to preserve some of the supersymmetry. In particular an N=(2,2) superconformal field theory is obtained from supersymmetry breaking due to the boundary from N=(4,4). In this case we calculate the central charge of the CFT and show its dependence on the topology of the Riemann surface.
Quantum hamiltonian reduction of affine superalgebras is studied in the twisted case. The Ramond sector of "minimal" superconformal W-algebras is described in detail, the determinant formula is obtained. Extensive list of examples includes all the simple Lie superalgebras of rank up to 2. The paper generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted case.
In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with $N\!-\!2$ supersymmetries, via quantum Hamiltonian reduction of the Lie superalgebras $osp(N|2)$. The motivation is to understand how one could systematically construct generalized string theories from superalgebras. We also briefly discuss the BRST algebra of the topological string, which is a doubly twisted $N\!=\!4$ superconformal algebra.
We find an N=1 gauge theory that flows to the rank-one N=2 superconformal field theory with $E_7$ flavor symmetry. We first obtain a Lagrangian description for the $R_{0, N}$ theory, which appears in the S-dual description of the SU(N) gauge theory with 2N fundamental hypermultiplets. This is a straightforward generalization of the proposed Lagrangian description for the $E_6$ theory. The $E_7$ theory is then obtained via partial Higgsing of the $R_{0, 4}$ theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on $S^2$…
We study the topologically twisted string theory on the general back-ground $AdS_3\times {\cal N}$ which is compatible with the world-sheet N=2 superconformal symmetry and is extensively discussed in the recent works (hep-th/9904024, hep-th/9904040). After summarizing the algebraic structure of the world-sheet topological theory, we show that the space-time (boundary) conformal theory should be also topological. We directly construct the space-time topological conformal algebra (twisted N=2 superconformal algebra) from the degrees of freedom in the world-sheet topological theory. Firstly, we w…
We show that almost all string theories, including the bosonic string, the superstring and $W$-string theories, possess a twisted N=2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the \brs operators of the $W_n$-string can be obtained by hamiltonian reduction of $SL(n|n-1)$. The tachyonic and ground ring states of $W$-strings are described in the light of the N=2 superconformal structure, and the ground ring generators for the non-critical $W_3$-string are expli…
We complete the program of 2012.15792 about perturbative approaches for $\mathcal{N}=2$ superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the p…
We introduce a suitable adapted ordering for the twisted N=2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-closed Verma modules they can only be one-dimensional. We give all singular vectors for the levels 1/2, 1, and 3/2 for both complete Verma modules and G-closed Verma modules. We also give explicit examples of d…
We present the construction of exactly solvable superconformal field theories describing Type II string models compactified on compact G_2 manifolds. These models are defined by anti-holomorphic quotients of the form (CY*S^1)/Z_2, where we realize the Calabi-Yau as a Gepner model. In the superconformal field theory the Z_2 acts as charge conjugation implying that the representation theory of a W(2,4,6,8,10) algebra plays an important role in the construction of these models. Intriguingly, in all three examples we study, including the quintic, the massless spectrum in the Z_2 twisted sector of …
We construct a string theory in three-dimensional anti-de Sitter space-time that is independent of the boundary metric. It is a topologically twisted theory of quantum gravity. We study string theories with an asymptotic N=2 superconformal symmetry and demonstrate that, when the world sheet coupling to the space-time boundary metric undergoes a U(1) R-symmetry twist, the space-time boundary energy-momentum tensor becomes topological. As a by-product of our analysis, we obtain the world sheet vertex operator that codes the space-time energy-momentum for conformally flat boundary metrics.
We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also be viewed as a topological algebra automorphism. In particular null vectors are mapped into null vectors, considerably simplifying their computation. We give the level 2 results. Finally we discuss the spectral flow mapping in the case of the DDK and KM realizations of the topological algebra.
We construct an embedding of two commuting copies of the N=2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kahler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kahler manifold. The classical limit of this result allows one to recover the celebrated generalized Kahle…
Vertex algebra of extended operators in 4d N=2 superconformal field theories
本文在4d N=2超共形场论中，通过拓扑下降从Schur算子构造扩展算子，证明其扩大顶点算子代数，并以自由超多重态为例计算扩展算子乘积展开。
Superconformal indices of $\mathcal{N}=4$ Chern-Simons matter theories
本文计算了由特殊SCFT构造的$\mathcal{N}=4$ Chern-Simons物质理论的超共形指标，推导其Coulomb/Higgs极限，确定真空模空间，用于检验镜像对称性。
We investigate the relation between N=(2,2) superconformal Lie group WZNW models and Lie supergroup WZNW models. The B-twist of an exactly marginal perturbation of the world-sheet superconformal sigma model is the supergroup model. Moreover, the superconformal currents are expressed in terms of Lie superalgebra currents in the twisted theory. As applications, we find protected sectors and boundary actions in the supergroup sigma model. A special example is the relation between string theory on AdS_3 x S^3 x T^4 in the RNS formalism and the U(1,1|2) x U(1|1) x U(1|1) supergroup WZNW model.
Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1,2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formall…
We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface $Σ$ and a three-manifold $M$, and show that when $Σ$ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on $M$. Based on these results, we establish a correspondence between three-dimensional $\mathcal{N} = 2$ superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmet…
We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to finding extended conformal symmetries. We describe a procedure of partial gauge fixing of these theories which leads generally to theories with superconformally extended ${\cal W}$-algebras. The pseudoparticle model allows one to derive the finite transformations of the gauge and matter fields occurring in these theories with extended conformal symmetries. …
In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the…
We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. …
Origami with a Twist: Twisted Holography of Four-Dimensional $\mathcal{N}=2$ Orientifold Theories
本文研究四维 $\mathcal{N}=2$ 超共形箭图规范理论，说明其来自定向折纸上的 D3-膜，并构造了体空间为 $\text{SL}_2 \mathbb{C} / Γ$ 卡拉比-丘三重流形的大 N 扭转全息对偶新例子。
We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal field theory of Argyres-Douglas type, obtained via twisted compactification of six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular puncture, by using spectral networks. We give strong evidence of the equivalence of $\mathcal{N}=2$ superconformal field theories from six-dimensional theories of different ranks by systematically comparing the chamber structure and wall-crossing phenomena.
The quantum SUSY N=1 hierarchy based on $sl(2|1)^{(2)}$ twisted affine superalgebra is considered. The construction of the corresponding Baxter's Q-operators and fusion relations is outlined. The relation with the superconformal field theory is discussed.
Superconformal Gravity And The Topology Of Diffeomorphism Groups
本文推广扭曲四维超对称杨-米尔斯理论，通过路径积分构造光滑四流形族的唐纳森不变量推广，并证明其可解释为耦合共形超引力背景场的拓扑扭曲路径积分，从而揭示微分同胚群的拓扑信息。
We study 4D N=2 superconformal field theories that arise from the compactification of 6D N=(2,0) theories of type D_N on a Riemann surface, in the presence of punctures twisted by a Z_2 outer automorphism. Unlike the untwisted case, the family of SCFTs is in general parametrized, not by M_{g,n}, but by a branched cover thereof. The classification of these SCFTs is carried out explicitly in the case of the D_4 theory, in terms of three-punctured spheres and cylinders, and we provide tables of properties of twisted punctures for the D_5 and D_6 theories. We find realizations of Spin(8) and Spin(…
Superconformal Indices of 3d $\mathcal{N}=2$ SCFTs and Holography
本研究探讨三维N=2超共形场论在类Cardy极限下的超共形指标，证明其前两项主导项由拓扑扭曲指标的贝特拟设表述决定，并将该关系应用于全息超共形场论推导闭式表达式，还讨论了对AdS₄黑洞熵及四维规范超引力修正的启示。
The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.
We construct the T duals of certain type IIA brane configurations with one compact dimension (elliptic models) which contain orientifold planes. These configurations realize four-dimensional $\NN=2$ finite field theories. For elliptic models with two negatively charged orientifold six-planes, the T duals are given by D3 branes at singularities in the presence of O7-planes and D7-branes. For elliptic models with two oppositely charged orientifold planes, the T duals are D3 branes at a different kind of orientifold singularities, which do not require D7 branes. We construct the adequate orientif…
Long-range to the Rescue of Yang-Baxter II
本文研究了四维超共形quiver规范论的自旋链模型，扩展分析了四磁子扇区并构造了显式特征向量，发现四磁子解可由三磁子解递归表示，且遵守无限塔的Yang-Baxter方程。
We study the spectrum of one single magnon in the superconformal beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including wrapping contributions at their critical order L.
We derive the planar dilatation operator in the closed subsector of scalar composite operators of an N=2 superconformal quiver gauge theory to three loops. By tuning the ratio of its two gauge couplings we interpolate between a Z_2 orbifold of N=4 SYM theory and N=2 superconformal QCD. We find zeta(3) contributions at three loops that disappear when the theory is at the orbifold point. They are responsible for imaginary contributions to the dispersion relation of a single scalar excitation in the spin-chain picture. This points towards an interpretation of the individual scalar excitations as …
Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We argue that nonperturbative dynamics of class S theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized Hitchin's equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or ho…
We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R^4, possibly in the presence of a codimension-two defect operator supported on R^2 \times C \subset M \times C. We expect this structure to survive the Ω-deformation.
We present a conjectural description of the space of local operators on a stack of finitely many fivebranes in $M$ theory at the level of the holomorphic twist. Our approach is through the lens of twisted holography and utilizes a description of the minimal twist of eleven-dimensional supergravity. We find that the spaces of local operators are modules for the exceptional linearly compact super Lie algebra $E(3|6)$. From the conjectural description of local operators we deduce closed formulas for the superconformal index of six-dimensional $\mathcal{N}=(2,0)$ theories of type $A_{N-1}$.
We study interacting massive N=(2,2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory with relevant operators, and twist the theory into a topological quantum field theory. These theories can be thought of as twisted Landau-Ginzburg models with negative power superpotential. We determine the structure constants of the chiral ring and therefore all correlators of these topological quantum field theories. We provide general formulas for the deformed operators of g…
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