scholarly journals Conformal block expansion in celestial CFT

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Alexander Atanasov ◽  
Walker Melton ◽  
Ana-Maria Raclariu ◽  
Andrew Strominger
Keyword(s):  
Conformal Block

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

scholarly journals Applications of alpha space

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Daniel Rutter ◽  
Balt C. van Rees
Keyword(s):  
Inversion Formula ◽  
Conformal Block ◽  
Definition Of

Abstract We extend the definition of ‘alpha space’ as introduced in [1] to two spacetime dimensions. We discuss how this can be used to find conformal block decompositions of known functions and how to easily recover several lightcone bootstrap results. In the second part of the paper we establish a connection between alpha space and the Lorentzian inversion formula of [2].

scholarly journals Efficient rules for all conformal blocks

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jean-François Fortin ◽  
Wen-Jie Ma ◽  
Valentina Prilepina ◽  
Witold Skiba
Keyword(s):  
Operator Product Expansion ◽  
General Procedure ◽  
Conformal Block ◽  
Irreducible Representations ◽  
Operator Product ◽  
Projection Operators ◽  
Space Operator ◽  
Conformal Blocks ◽  
General Rules

Abstract We formulate a set of general rules for computing d-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism [1]. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars S and some specific irreducible representations R, namely 〈SSSS〉, 〈SSSR〉, 〈SRSR〉 and 〈SSRR〉 (where, when allowed, R is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.

scholarly journals SEIBERG–WITTEN PREPOTENTIAL FROM WZNW CONFORMAL BLOCK: LANGLANDS DUALITY AND SELBERG TRACE FORMULA

2012 ◽  
Vol 27 (22) ◽  
pp. 1250129
Author(s):  
TA-SHENG TAI
Keyword(s):  
Trace Formula ◽  
Conformal Block ◽  
Selberg Trace Formula ◽  
Conformal Blocks ◽  
Langlands Duality

We show how SU(2) Nf = 4 Seiberg–Witten prepotentials are derived from [Formula: see text] four-point conformal blocks via considering Langlands duality.

scholarly journals Classical Virasoro irregular conformal block

2015 ◽  
Vol 2015 (7) ◽  
Author(s):  
Chaiho Rim ◽  
Hong Zhang
Keyword(s):  
Conformal Block

scholarly journals Irregular conformal block, spectral curve and flow equations

2016 ◽  
Vol 2016 (3) ◽  
Author(s):  
Sang Kwan Choi ◽  
Chaiho Rim ◽  
Hong Zhang
Keyword(s):  
Spectral Curve ◽  
Conformal Block ◽  
Flow Equations
Sign in / Sign up

Export Citation Format

Share Document