相关论文: A direct proof of AGT conjecture at beta = 1
The representation theories of the SU(2)$_k$-extended $N$=4 superconformal algebras (SCAs) with $arbitrary$ level $k$ are developed being based on their Feigin-Fuchs representations found recently by the present author. A basic unit of the…
It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large $N$ arguments for this duality can formally be used to…
We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex symmetric sets with respect to the Gaussian measure. Namely, letting $J_{k-1}(s)=\int^s_0 t^{k-1} e^{-\frac{t^2}{2}}dt$ and $c_{k-1}=J_{k-1}(+\infty)$,…
The Nekrasov-Shatashvili limit of beta-ensembles with polynomial potential and N=2 supersymmetric gauge theories in the Omega-background is intimately related to complex one-dimensional quantum mechanics. Multi-instanton corrections in…
We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition function. The positive intertwiner is the…
Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…
Within the set of schemes defined by generalized, manifestly gauge invariant exact renormalization groups for QED, it is argued that the beta-function in the four dimensional massless theory cannot possess any nonperturbative power…
We consider the GUT compatible formulation of noncommutative QED, as well as noncommutative SU(N) GUTs, for N>2, with no scalars but with fermionic matter in an arbitrary, anomaly-free representation, in the enveloping algebra approach. We…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This…
We investigate some peculiarities in the calculation of the two-loop beta-function of $N=1$ supersymmetric models which are intimately related to the so-called "Anomaly Puzzle". There is an apparent paradox when the computation is performed…
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…
We discuss qualitative behavior of the SU(N) gauge beta functions in QCD with many massless flavors. Non-perturbative beta functions can be obtained by extracting the renormalized trajectories in the exact renormalization group framework.…
We provide a uniform solution to 4d N=2 gauge theory with a single gauge group G=A,D,E when the one-loop contribution to the beta function from any irreducible component R of the hypermultiplets is less than or equal to half of that of the…
In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a…
There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until…
We elaborate on a recently conjectured relation of Painlev\'e transcendents and 2D CFT. General solutions of Painlev\'e VI, V and III are expressed in terms of $c=1$ conformal blocks and their irregular limits, AGT-related to instanton…
The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT…
Let $S_n$ denote the symmetric group on $n$ elements, and $\Sigma\subseteq S_{n}$ a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Richthammer [arXiv:0906.1238], states that if $\Sigma$ is a…
We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of…
According to the Svetitsky-Yaffe conjecture, a (d+1)-dimensional pure gauge theory undergoing a continuous deconfinement transition is in the same universality class as a d-dimensional statistical model with order parameter taking values in…