scholarly journals CONFORMAL BLOCKS AS DOTSENKO–FATEEV INTEGRAL DISCRIMINANTS

2010 ◽  
Vol 25 (16) ◽  
pp. 3173-3207 ◽  
Author(s):  
A. MIRONOV ◽  
A. MOROZOV ◽  
SH. SHAKIROV
Keyword(s):  
Matrix Models ◽  
Spherical Functions ◽  
Parametric Family ◽  
Point Function ◽  
Conformal Blocks ◽  
Level 3 ◽  
Similar Description

As anticipated in Ref. 1, elaborated in Refs. 2–4, and explicitly formulated in Ref. 5, the Dotsenko–Fateev integral discriminant coincides with conformal blocks, thus providing an elegant approach to the AGT conjecture, without any reference to an auxiliary subject of Nekrasov functions. Internal dimensions of conformal blocks in this identification are associated with the choice of contours: parameters of the Dijkgraaf–Vafa phase of the corresponding matrix models. In this paper, we provide further evidence in support of this identity for the 6-parametric family of the 4-point spherical conformal blocks, up to level 3 and for arbitrary values of external dimensions and central charges. We also extend this result to multipoint spherical functions and comment on a similar description of the 1-point function on a torus.

scholarly journals ON THE SCHWINGER–DYSON EQUATIONS FOR A VERTEX MODEL COUPLED TO 2-D GRAVITY

1995 ◽  
Vol 10 (08) ◽  
pp. 695-707
Author(s):  
AL. KAVALOV
Keyword(s):  
Matrix Models ◽  
Extrinsic Curvature ◽  
Vertex Model ◽  
Point Function ◽  
Lattice Gauge ◽  
Planar Limit ◽  
Dimensional Gravity ◽  
Free Case ◽  
Lattice Gauge Theories ◽  
Perturbative Corrections

We consider a two-matrix model with the interaction involving the term tr ABAB, which is quartic in angular variables. It describes a vertex model (in particular — of F-model type) on the lattice of fluctuating geometry and is the simplest representative of the class of matrix models describing coupling to two-dimensional gravity of general vertex models. This class includes most of the physically interesting matrix models, such as lattice gauge theories and matrix models describing extrinsic curvature strings. We show that the system of loop (Schwinger–Dyson) equations of the model decouples in the planar limit and allows one to find closed equations for arbitrary correlators, including the ones involving angular variables. We write down the equations for the two-point function and the eigenvalue density and sketch the calculation of perturbative corrections to the free case

scholarly journals TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS

2012 ◽  
Vol 27 (01) ◽  
pp. 1230001 ◽  
Author(s):  
A. MIRONOV ◽  
A. MOROZOV ◽  
SH. SHAKIROV
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Model Problem ◽  
Conformal Blocks ◽  
Model Approach

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko–Fateev β-ensemble averages and Nekrasov functions by a double deformation of the exponentiated Seiberg–Witten prepotential in β≠1 and gs≠0 directions. Establishing the equality of these two quantities is a typical matrix model problem.

scholarly journals The O(N ) model with ϕ6 potential in ℝ2 × ℝ+

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Christopher P. Herzog ◽  
Nozomu Kobayashi
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Stress Tensor ◽  
The Other ◽  
Three Dimensions ◽  
Planar Boundary ◽  
Point Function ◽  
Conformal Blocks ◽  
Boundary Limit ◽  
The Stability

Abstract We study the large N limit of O(N ) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N . We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.

scholarly journals A tree-level 3-point function in the su(3)-sector of planar $ \mathcal{N}=4 $ SYM

2013 ◽  
Vol 2013 (10) ◽  
Author(s):  
Omar Foda ◽  
Yunfeng Jiang ◽  
Ivan Kostov ◽  
Didina Serban
Keyword(s):  
Tree Level ◽  
Point Function ◽  
Level 3

scholarly journals Recursion relations for 5-point conformal blocks

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
David Poland ◽  
Valentina Prilepina
Keyword(s):  
Linear Combination ◽  
Energy Operator ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Expectation Value ◽  
Conformal Field ◽  
Weight Shifting

Abstract We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

Sign in / Sign up

Export Citation Format

Share Document