scholarly journals Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions

2016 ◽  
Vol 2016 (3) ◽  
Author(s):  
Vasyl Alba ◽  
Kenan Diab
Keyword(s):  
Higher Spin Symmetry ◽  
Spin Symmetry ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

scholarly journals Four point functions in CFT’s with slightly broken higher spin symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joao A. Silva
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Higher Spin Symmetry ◽  
Three Dimensional ◽  
Spin Current ◽  
Spin Symmetry ◽  
Trace Operator ◽  
Conformal Field ◽  
Higher Spin ◽  
Single Trace

Abstract We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite t’Hooft coupling. More concretely, we obtain a formula for $$ \left\langle {j}_s{j}_{\tilde{0}}{j}_{\tilde{0}}{j}_{\tilde{0}}\right\rangle $$ j s j 0 ˜ j 0 ˜ j 0 ˜ , where js is a higher spin current and $$ {j}_{\tilde{0}} $$ j 0 ˜ is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all spinning four point functions in these theories.

scholarly journals The Schwarzian sector of higher spin CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shouvik Datta
Keyword(s):  
Spectral Decomposition ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Virasoro Symmetry ◽  
Higher Spin ◽  
Extremal Limit ◽  
Conserved Currents

Abstract Two-dimensional conformal field theories with Virasoro symmetry generically contain a Schwarzian sector. This sector is related to the near-horizon region of the near-extremal BTZ black hole in the holographic dual. In this work we generalize this picture to CFTs with higher spin conserved currents. It is shown that the partition function in the near-extremal limit agrees with that of BF higher spin gravity in AdS2 which is described by a generalized Schwarzian theory. We also provide a spectral decomposition of Schwarzian partition functions via the $$ {\mathcal{W}}_N $$ W N fusion kernel and consider supersymmetric generalizations.

scholarly journals GELFAND–DICKEY ALGEBRA AND HIGHER SPIN SYMMETRIES ON T2 = S1 × S1

2008 ◽  
Vol 23 (31) ◽  
pp. 5059-5080
Author(s):  
M. B. SEDRA
Keyword(s):  
Integrable Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Dimensional Torus ◽  
Conformal Field ◽  
Generalized Symmetries ◽  
Higher Spin

In this work we aim to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two-dimensional torus T2. We show explicitly, in a consistent way, how one can extract these generalized symmetries from the Gelfand–Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed.

scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

HIGHER SPIN SYMMETRY AND SU(2) WZNW MODEL

1994 ◽  
Vol 09 (26) ◽  
pp. 2389-2398
Author(s):  
SASANKA GHOSH
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Higher Spin Symmetry ◽  
Symmetry Algebra ◽  
Spin Symmetry ◽  
Conformal Field ◽  
Large N ◽  
Wznw Model ◽  
Higher Spin

Generators of an infinite number of conserved charges of the integrable SU(2) WZNW model are identified with the generators of a W1+∞ symmetry algebra. This integrable conformal field theory also describes the ZN symmetric Ising model at the critical point in the large-N limit.

INFINITE DIMENSIONAL ALGEBRAS AND 2+1 DIMENSIONAL FIELD THEORY: YET ANOTHER VIEW OF gl(∞) SOME NEW ALGEBRAS

1990 ◽  
Vol 02 (02) ◽  
pp. 193-200 ◽  
Author(s):  
JENS HOPPE
Keyword(s):  
Braid Groups ◽  
Theoretical Physics ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Associative Algebras ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Higher Spin ◽  
Associative Structures ◽  
Area Preserving

Over the past years, associative algebras have come to play a major role in several areas of theoretical physics. Firstly, it has been realized that Yang Baxter algebras [1] constitute the relevant structure underlying 1+1 dimensional integrable models; in addition, their relation to braid groups, the theory of knots and links, and the exchange algebras of 1+1 dimensional conformal field theories [2] has been quite well understood by now. Secondly, deformations of Poisson structures that appeared in 2+1 dimensional field theories as infinite dimensional symmetry algebras possess underlying associative structures, which have also been studied in some detail (concerning higher spin theories see, e.g., [3, 4] and references therein, concerning the enveloping algebra of sl(2, C) see, e.g., [5], concerning deformations of diff AT2 — the Lie algebra of infinitesimal area preserving diffeomorphisms of the Torus — see [6, 7, 8, 9]). Ideas on how both investigations could eventually converge (i.e., a relation between 2+1 and 1+1 dimensions) have, e.g., been expressed in [10]. As indicated by the two subtitles there will be two parts to my paper: the first one presents a view on something I met long ago [11], and recently got interested in again [5, 7, 9, 12], while the second part introduces some algebraic structures that seem to be interesting, and possibly new.

Sign in / Sign up

Export Citation Format

Share Document