scholarly journals State-operator correspondence in celestial conformal field theory

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Erin Crawley ◽  
Noah Miller ◽  
Sruthi A. Narayanan ◽  
Andrew Strominger
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Inner Product ◽  
Conformal Field ◽  
State Operator ◽  
Inner Products ◽  
Boundary States ◽  
Celestial Sphere ◽  
New Entry

Abstract The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

scholarly journals CONFORMAL INVARIANCE ON ORBIFOLDS AND EXCITATIONS OF SINGULARITY

2009 ◽  
Vol 24 (26) ◽  
pp. 2089-2097 ◽  
Author(s):  
ZHENG YIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Conformal Invariance ◽  
Two Dimensional ◽  
Conformal Field ◽  
Boundary States ◽  
Physical Effects

We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps. Representative classes of singularities can be described exactly using generalizations of boundary states. From this we compute correlation functions and derive the spectra of excitations localized at the singularities.

DEGENERATE AFFINE HECKE ALGEBRAS AND TWO-DIMENSIONAL PARTICLES

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 109-140 ◽  
Author(s):  
IVAN CHEREDNIK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Quantum Groups ◽  
Hecke Algebras ◽  
Two Dimensional ◽  
Conformal Field ◽  
Affine Hecke Algebras ◽  
The Difference ◽  
Zamolodchikov Equation

We demonstrate that the quantization of momenta in different two dimensional theories of elementary particles with factorizable scattering amplitudes gives the so-called degenerate affine Hecke algebras and their versions. Some connections with quantum groups(Yangians), the two-dimensional conformal field theory and representation theory am discussed. In particular, an interpretation and generalizations of the difference counterpart of the Knizhnik-Zamolodchikov equation are found by means of the particles on a segment.

BOUNDARY STATES IN BOUNDARY LCFT: AN ALGEBRAIC APPROACH

2003 ◽  
Vol 18 (25) ◽  
pp. 4639-4654 ◽  
Author(s):  
YUKITAKA ISHIMOTO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Cell Structure ◽  
Algebraic Approach ◽  
Open String ◽  
Closed String ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Boundary States ◽  
Rank 2

It is well known that LCFT generally contains Jordan cell structure and, in our previous paper, we have proposed a conjecture that one and only one boundary sate is allowed in the rank-2 cell. With these states in c=-2 rational LCFT, we can express boundary states in the closed string picture, in regard to corresponding boundary conditions in the open string picture. In this paper, We briefly review our previous paper on boundary states in LCFTs. We also add one more proof which supports the conjecture, and confirm this doesn't change our previous results. This paper is based on the talk given at School & Workshop On Logarithmic Conformal Field Theory and Its Applications held in Tehran, Iran.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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