Related papers: Five-dimensional AGT Conjecture and the Deformed V…
We study a gauge theory in a 5D warped space via the dimensional deconstruction that a higher dimensional gauge theory is constructed from a moose of 4D gauge groups. By the AdS/CFT correspondence, a 5D warped gauge theory is dual to a 4D…
Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…
Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain…
We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out…
All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has…
Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite theories the AGT conjecture favours…
The phase diagram of five-dimensional anisotropic gauge theories in a flat background has been extensively explored during the last decade. Here, we present novel results for the phase structure of the five-dimensional anisotropic SU(2)…
We investigate the high-energy behavior of the scattering amplitudes in the extra dimensional gauge theory where the gauge symmetry is broken by the boundary condition. We study, in particular, the 5-dimensional SU(5) grand unified theory…
We study the dual descriptions recently discovered for the Seiberg-Witten theory in the presence of surface operators. The Nekrasov partition function for a four-dimensional N=2 gauge theory with a surface operator is believed equal to the…
We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge theory on A1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation.…
We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized dyrectly in the SG…
In this article we consider the local supersymmetry breaking and the broken SU(5) symmetry permisible by dilaton vacuum configuration in supergravity theories. We establish the parameter relation of spontaneuos breaking of supersymmetry and…
This is the 12th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories" ed. J. Teschner. This article describes one way to understand an important part of the AGT-correspondence in terms of a triality…
The best way to represent generic conformal blocks is provided by the free-field formalism, where they acquire a form of multiple Dotsenko-Fateev-like integrals of the screening operators. Degenerate conformal blocks can be described by the…
We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM…
A relationship between 4d gauge theory and 2d CFT will be reviewed from the very basics. We will first cover the introductory material on the 2d CFT and on the instantons of 4d gauge theory. Next we will explicitly calculate and check the…
We study Gauge-Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2) pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly…
We review the holomorphic block factorisation of partition functions of supersymmetric theories on compact manifolds in various dimensions. We then show how to interpret 3d and 5d partition functions as correlation functions with underlying…
We give some evidences of the AGT-W relation between SU(3) quiver gauge theories and A_2 Toda theory. In particular, we derive the explicit form of 5-point correlation functions in the lower orders and confirm the agreement with Nekrasov's…
We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the N=2 superconformal algebra. Our construction uses two ingredients: (i) the relation between the representation theories of the…