scholarly journals The conformal anomaly action to fourth order (4T) in $$d=4$$ in momentum space

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio ◽  
Dimosthenis Theofilopoulos
Keyword(s):  
Momentum Space ◽  
Form Factors ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Independent Form ◽  
Stress Energy ◽  
Complete Determination ◽  
Non Local

AbstractWe elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $$R\square ^{-1}$$ R □ - 1 interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

scholarly journals Spontaneously broken boosts in CFTs

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Zohar Komargodski ◽  
Márk Mezei ◽  
Sridip Pal ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Surface States ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Scaling Dimension ◽  
Large Charge

Abstract Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as O(1). We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.

scholarly journals ON THE CONFORMAL ANOMALY FROM HIGHER DERIVATIVE GRAVITY IN AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (03) ◽  
pp. 413-428 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Einstein Gravity ◽  
Low Energy ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Higher Derivative

We follow Witten's proposal1 in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above (d + 1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L =aR2 + bRμνRμν + Λ (even when a=0 or b=0) is five-dimensional bulk theory for [Formula: see text] super-Yang–Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of [Formula: see text] supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).

scholarly journals Momentum space parity-odd CFT 3-point functions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Momentum Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field ◽  
Weight Shifting ◽  
Conserved Currents

Abstract We study the parity-odd sector of 3-point functions comprising scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of some of these correlators. Wherever divergences appear we discuss their regularisation and renormalisation using appropriate counter-terms.

Form Factor Perturbation Theory

2020 ◽  
pp. 863-881
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Perturbation Theory ◽  
Form Factor ◽  
Mass Spectrum ◽  
Cross Sections ◽  
Form Factors ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Sine Gordon Model ◽  
First Order Perturbation

Chapter 22 introduces a perturbative technique based on the form factors to study non-integrable models. These models often include stumbling blocks like decays and production scattering processes, confinement phenomena and nucleation of false vacua, resonance peaks in the cross sections, etc. All these physical aspects are usually accompanied by a great mathematical complexity. However, the perturbative technique permits the computation of the corrections to the mass spectrum, the vacuum energy, the scattering amplitudes and so on. This chapter discusses in depth multiple deformations of the conformal field theories, form factor perturbation theory, first-order perturbation theory, non-locality and confinement of the excitations and the multi-frequency Sine–Gordon model.

The conformal anomaly and anomaly-induced action

2021 ◽  
pp. 414-424
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Effective Action ◽  
Black Hole Physics ◽  
Dimensional Regularization ◽  
Form Factors ◽  
Simple Calculation ◽  
Conformal Anomaly ◽  
Local Form ◽  
Conformal Transformations ◽  
Transformation Rules ◽  
Non Local

This chapter describes in detail basic results concerning the conformal (trace) anomaly and anomaly-induced action in four spacetime dimensions. It is shown how the anomaly appears from the non-local form factors discussed in chapter 16. Starting from the conformal transformations, the necessary invariants and transformation rules are obtained. The simplest derivation of the anomaly in dimensional regularization is explained, followed by the equally simple calculation of the anomaly-induced effective action of gravity. The chapter also briefly discusses applications of the induced effective action in cosmology and black hole physics.

scholarly journals QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

2005 ◽  
Vol 17 (05) ◽  
pp. 577-612 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER ◽  
STEFAN HOLLANDS
Keyword(s):  
Field Theories ◽  
Positive Energy ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Conformal Field ◽  
Quantum Energy Inequalities ◽  
Stress Energy

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

BRST EXACTNESS OF STRESS-ENERGY TENSORS

1994 ◽  
Vol 09 (12) ◽  
pp. 2033-2065 ◽  
Author(s):  
HIDEO MIYATA ◽  
HIROSHI SUGIMOTO
Keyword(s):  
Lie Algebras ◽  
Simple Root ◽  
Dynkin Diagram ◽  
Field Theories ◽  
General Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Stress Energy ◽  
Multiple Integrals ◽  
Extended Dynkin Diagram

BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

scholarly journals $$ T\overline{T} $$ Deformation of stress-tensor correlators from random geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shinji Hirano ◽  
Tatsuki Nakajima ◽  
Masaki Shigemori
Keyword(s):  
Stress Tensor ◽  
Salient Feature ◽  
Two Dimensions ◽  
Operator Product ◽  
Conformal Anomaly ◽  
Logarithmic Correction ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Random Geometry ◽  
Liouville Action

Abstract We study stress-tensor correlators in the $$ T\overline{T} $$ T T ¯ -deformed conformal field theories in two dimensions. Using the random geometry approach to the $$ T\overline{T} $$ T T ¯ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $$ T\overline{T} $$ T T ¯ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $$ T\overline{T} $$ T T ¯ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $$ T\overline{T} $$ T T ¯ -deformed operator product expansions of the stress tensor. A salient feature of the $$ T\overline{T} $$ T T ¯ -deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.

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