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 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 Strongly γ -Deformed N=4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory

2018 ◽  
Vol 120 (11) ◽  
Author(s):  
David Grabner ◽  
Nikolay Gromov ◽  
Vladimir Kazakov ◽  
Gregory Korchemsky
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Yang Mills ◽  
Conformal Field

The search for higher symmetry in string theory

1989 ◽  
Vol 329 (1605) ◽  
pp. 349-357 ◽  
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Vantage Point ◽  
Higher Symmetry ◽  
Conformal Field ◽  
Soluble Model ◽  
Higher Dimensional ◽  
Dimensional Gravity

Some remarks are made about the nature and role of the search for higher symmetry in string theory. These symmetries are most likely to be uncovered in a mysterious ‘unbroken phase’, for which (2+ 1)-dimensional gravity provides an interesting and soluble model. New insights about conformal field theory, in which one gets ‘out of flatland’ to see a wider symmetry from a higher-dimensional vantage point, may offer clues to the unbroken phase of string theory

scholarly journals 4-point function from conformally coupled scalar in AdS6

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jae-Hyuk Oh
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Ward Identity ◽  
Conformal Symmetry ◽  
Classical Solutions ◽  
Point Function ◽  
Conformal Theory ◽  
Conformal Field ◽  
Linear Limit

Abstract We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

scholarly journals The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Mattia Cesàro ◽  
Gabriel Larios ◽  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Yang Mills ◽  
Conformal Field ◽  
Operator Spectrum ◽  
Two Parameter ◽  
Kaluza Klein

Abstract A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large-N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N, this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side.

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.

2D SIGMA MODEL APPROACH TO 4D INSTANTONS

1992 ◽  
Vol 07 (07) ◽  
pp. 1415-1447 ◽  
Author(s):  
Q-HAN PARK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Sigma Model ◽  
Gauge Groups ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Toda Field Theory ◽  
Model Approach

4D self-dual theories are proposed to generalize 2D conformal field theory. We identify 4D self-dual gravity as well as self-dual Yang-Mills theory with 2D sigma models valued in infinite-dimensional gauge groups. It is shown that these models possess infinite-dimensional symmetries with associated algebras—“CP1 extensions” of respective gauge algebras of 2D sigma models—which generalize the Kac-Moody algebra as well as W∞. We address various issues concerning 2D sigma models, twistors and sheaf cohomology. An attempt to connect 4D self-dual theories with 2D conformal field theory is made through sl (∞) Toda field theory.

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