scholarly journals Two Applications of the Analytic Conformal Bootstrap: A Quick Tour Guide

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 247
Author(s):  
Agnese Bissi ◽  
Parijat Dey ◽  
Giulia Fardelli
Keyword(s):  
Operator Product ◽  
Analytic Structure ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Large N ◽  
Fisher Model ◽  
Recent Developments ◽  
Analytic Aspect

We reviewed the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are solely based on symmetries, particularly on the analytic structure and in the associativity of the operator product expansion. We focused on two applications of the analytic conformal bootstrap: the study of the ϵ expansion of the Wilson–Fisher model via the introduction of a dispersion relation and the large N expansion of the maximally supersymmetric Super Yang–Mills theory in four dimensions.

scholarly journals ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES

2001 ◽  
Vol 16 (16) ◽  
pp. 2747-2769 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Gauge Theories ◽  
De Sitter Space ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Classical Geometry ◽  
Large N ◽  
Quantum Phenomena

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

scholarly journals Boundary conformal field theory at large charge

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Gabriel Cuomo ◽  
Márk Mezei ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Background Field ◽  
Effective Field ◽  
Three Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Fisher Model ◽  
Large Charge

Abstract We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

scholarly journals On the Trace Anomaly of the Chaudhuri–Choi–Rabinovici Model

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 276
Author(s):  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Four Dimensions ◽  
Conformal Field ◽  
Trace Anomaly ◽  
Large N ◽  
Marginal Deformation

Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large N limit was constructed by Chaudhuri–Choi–Rabinovici. On a non-supersymmetric conformal manifold, the c coefficient of the trace anomaly in four dimensions would generically change. In this model, we, however, find that it does not change in the first non-trivial order given by three-loop diagrams.

4-D SELF-DUAL INSTANTONS FROM 2-D SIGMA MODEL

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 781-789 ◽  
Author(s):  
Q-HAN PARK
Keyword(s):  
Sigma Model ◽  
Field Theories ◽  
Maxwell System ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Integrable Deformation ◽  
Large N ◽  
Higher Dimensional

4-d self-dual gravity and Yang-Mills theories are identified with 2-d sigma models taking values in infinite dimensional groups. This allows us to view 4-d self-dual theories as "large N limits" of 2-d conformal field theories. We also find a possible "integrable deformation" of 4-d self-dual gravity leading to the Einstein-Maxwell system and discuss its implication in the context of higher dimensional integrability.

COUPLING THE WESS-ZUMINO-WITTEN MODEL TO YANG-MILLS FIELDS

1991 ◽  
Vol 06 (11) ◽  
pp. 969-976 ◽  
Author(s):  
C.M. HULL ◽  
B. SPENCE
Keyword(s):  
Effective Action ◽  
Dimensional Space ◽  
Low Energy ◽  
Field Theories ◽  
Gauge Fields ◽  
Conformal Field Theories ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field

The coupling of the 2n-dimensional Wess-Zumino-Witten action to gauge fields is discussed and a simple manifestly gauge-invariant form of the gauged Wess-Zumino term is found which is an integral over a (2n+1)-dimensional space whose boundary is space-time. In two and four dimensions, our actions give simple forms for the action describing coset conformal field theories and the low-energy QCD effective action, respectively.

scholarly journals Causality, crossing and analyticity in conformal field theories

2021 ◽  
pp. 2150177
Author(s):  
Jnanadeva Maharana
Keyword(s):  
Operator Product Expansion ◽  
Scalar Fields ◽  
Field Theories ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Local Commutativity ◽  
Conformal Bootstrap ◽  
Wightman Functions ◽  
Wightman Axioms

Analyticity and crossing properties of four-point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial role of microcausality in deriving analyticity domains is discussed and domains of analyticity are presented. A pair of permuted Wightman functions are envisaged. The crossing property is derived by appealing to the technique of analytic completion for the pair of permuted Wightman functions. The operator product expansion of a pair of scalar fields is studied and analyticity property of the matrix elements of composite fields, appearing in the operator product expansion, is investigated. An integral representation is presented for the commutator of composite fields where microcausality is a key ingredient. Three fundamental theorems of axiomatic local field theories; namely, PCT theorem, the theorem proving equivalence between PCT theorem and weak local commutativity and the edge-of-the-wedge theorem are invoked to derive a conformal bootstrap equation rigorously.

scholarly journals Instantons beyond topological theory. I

2011 ◽  
Vol 10 (3) ◽  
pp. 463-565 ◽  
Author(s):  
E. Frenkel ◽  
A. Losev ◽  
N. Nekrasov
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Mechanical Models ◽  
Perturbative Corrections

AbstractMany quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of one-dimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang–Mills theory. In Part III we will discuss non-supersymmetric models.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

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