We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111}, M^{32} with N=2,3 supersymmetries and compare them with the corresponding dual gravity indices. For N^{010}, we find perfect agreements. In addition, for N^{010}/Z_k, we also find an agreement with the gravity index including the contributions from two types of D6-branes wrapping RP^3. For Q^{111}, we find that the model obtained by adding fundamental flavors to the N=6 theory has the right structure to be the correct model. For M^{32}, we find the matching with the gravity index modulo contributions from peculiar saddle points.
We explore aspects of the correspondence between Seifert 3-manifolds and 3d $\mathcal{N}=2$ supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d $\mathcal{N}=2$ theories constructed from boundary conditions and interfaces in a 4d $\mathcal{N}=2^*$ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d $\mathcal{N}=2^*$ theory. In th…
By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d $(2,0)$ theory on a three-manifold $M_3$. This generalization is applicable to both the 3d $\mathcal{N}=2$ and $\mathcal{N}=1$ supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by $M_3$. This is carried out in detail for $M_3$ a Seifert manifold, where we compute a refined version of the Witten index. In the context of…
We extend the definition of the refined topological vertex C to an n-coloured refined topological vertex C_n that depends on n free bosons, and compute the 5D strip partition function made of N pairs of C_n vertices and conjugate C*_n vertices. Using geometric engineering and the AGT correspondence, the 4D limit of this strip partition function is identified with a (normalized) matrix element of a (primary state) vertex operator that intertwines two (arbitrary descendant) states in a (generically non-rational) 2D conformal field theory with Z_n parafermion primary states.
We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d $\mathcal{N}=1$ gauge theories which can be realized as 5-brane webs with ON-planes, which include $D$-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely …
Refined Painlevé/gauge theory correspondence and quantum tau functions
International School for Advanced Studies (SISSA)（高级研究国际学院）；National Institute for Nuclear Physics (INFN), Section of Trieste（意大利国家核物理研究所的里雅斯特分部）；Institute for Geometry and Physics (IGAP)（几何与物理研究所）
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 calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries.
Conformal Anomaly for Dilaton Coupled Theories from AdS/CFT Correspondence
利用AdS/CFT对应，从超重力的角度，发现了在非零的弯曲背景下，作为红外效应的耦合共形理论的迹线异常。对于$d=2$，它与膨胀子耦合标量的共形异常（直到已知不明确的总导数项）相一致。在四维情形下，我们得到了${\cal N}=4$ super YM理论与共形超引力相互作用的共形反常。同样地，在更高的维度中，与声子相关的共形反常的计算似乎比使用标准QFT方法容易得多。
Instantons in N=4 Sp(N) and SO(N) theories and the AdS/CFT correspondence
在SU（N）规范群理论的基础上，我们对N=4的超对称规范理论中的ADHM多瞬子测度进行了大N鞍点近似.对于Sp（N），我们发现鞍点只存在于偶瞬子荷区。对于Sp（N）或SO（N），鞍点解参数化了AdS_5 x RP ^[5]，即这些理论的AdS/CFT对应中的对偶超引力几何。大N时的瞬子测度具有10维N=1超对称规范理论的配分函数的形式，其中幺正规范群的维数降为零。
Wilson loops in (p+1)-dimensional Yang-Mills theories using gravity/gauge theory correspondence
利用引力/规范理论对应，计算了（p+1）维Yang-Mills理论强耦合等离子体中类时和类光威尔逊圈的期望值.由类时威尔逊圈得到了偶极以任意速度0<v 1穿过等离子体时的速度相关夸克-反夸克势<1 and also obtain expressions for the screening lengths. When the velocity v-->，威尔逊圈变为类光，并得到了强耦合等离子体中喷流猝灭参数的形式。
We present a new expression for the partition function of refined Chern-Simons theory on $S^3$ with arbitrary gauge group, which is explicitly equal to $1$, when the coupling constant is zero. Using this form of partition function we show that the previously known Krefl-Schwarz representation of partition function of refined Chern-Simons theory on $S^3$ can be generalized to all simply-laced algebras. For all non-simply-laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at …
We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional N=2 U(2) gauge theories coupled to (A_1,D_{2n}) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A_1,D_{2n}) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A_3,A_3) theory to find …
This is the 10th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It reviews correspondences between three-dimensional gauge theories and complex Chern-Simons theory on suitable three-manifolds. Such correspondences are in many cases deeply related to the 4d/2d correspondence discussed in this collection. The partition functions of the three-dimensional gauge theories are calculable by means of localisation (as discussed in article no. 9 by K. Hosomichi), and the results are related to the quantum theory obtained by quantisation of Hitc…
The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization of the modular transformation matrices of $(2N+3,2)$ minimal models are proposed to compute the full Coulomb branch index of $(A_{1},A_{2N})$ Argyres-Douglas theories on the same space. Morever, M-theory construction of these theories suggests direct connection to the refined Chern-Simons theory. The connection is made precise by showing how the modular tra…
A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stress-energy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary e…
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
We characterize the correspondence between the twisted $N=2$ super-Yang-Mills theory and the Baulieu-Singer topological theory quantized in the self-dual Landau gauges. While the first is based on an on-shell supersymmetry, the second is based on an off-shell Becchi-Rouet-Stora-Tyutin symmetry. Because of the equivariant cohomology, the twisted $N=2$ in the ultraviolet regime and Baulieu-Singer theories share the same observables, the Donaldson invariants for 4-manifolds. The triviality of the Gribov copies in the Baulieu-Singer theory in these gauges shows that working in the instanton moduli…
We consider Type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and $N_f$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the ADHM method. We also discuss a particular tuning of Kähler parameters associated with this Higgsing.
