scholarly journals GEOMETRICAL PROPERTIES OF CONFORMAL FIELD THEORIES COUPLED TO TWO-DIMENSIONAL QUANTUM GRAVITY

1996 ◽  
Vol 11 (11) ◽  
pp. 1913-1928 ◽  
Author(s):  
S. BRAUNE
Keyword(s):  
Functional Integral ◽  
Quasiclassical Approximation ◽  
Conformal Field Theories ◽  
Point Function ◽  
World Sheet ◽  
Geometrical Properties ◽  
Conformal Field ◽  
Noncritical Strings ◽  
Scaling Dimension ◽  
Distance Variable

In this work we discuss an approach due to F. David to the geometry of world sheets of noncritical strings in quasiclassical approximation. The gravitational dressed conformal dimension is related to the scaling behavior of the two-point function with respect to a distance variable. We show how this approach can reproduce the standard gravitational dressing in the next order of perturbation theory. Furthermore, we try to find this scaling dimension by studying the functional integral. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet.

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 Scalar Dyon Production In Near Extremal Kerr-Newman Black Holes

2018 ◽  
Vol 168 ◽  
pp. 01011
Author(s):  
Chiang-Mei Chen ◽  
Sang Pyo Kim ◽  
Jia-Rui Sun ◽  
Fu-Yi Tang
Keyword(s):  
Black Holes ◽  
Pair Production ◽  
Cross Section ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Cross Section Ratio ◽  
Point Function ◽  
Charged Scalar ◽  
Conformal Field ◽  
Horizon Geometry

The pair production of charged scalar dyons is analytically studied in near-extremal Kerr-Newman (KN) dyonic black holes. The pair production rate and its thermal interpretation are given. Moreover, the absorption cross section ratio has been compared with the two-point function of the conformal field theories (CFTs) holographically dual to the near horizon geometry, namely warped AdS3, of the near extremal Kerr-Newman black holes to verify the threefold dyonic KN/CFTs correspondence.

scholarly journals Holographic BCFTs and communicating black holes

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hao Geng ◽  
Severin Lüst ◽  
Rashmish K. Mishra ◽  
David Wakeham
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Conformal Field ◽  
Theory Calculation ◽  
Scaling Dimension

Abstract We study the AdS/BCFT duality between two-dimensional conformal field theories with two boundaries and three-dimensional anti-de Sitter space with two Karch-Randall branes. We compute the entanglement entropy of a bipartition of the BCFT, on both the gravity side and the field theory side. At finite temperature this entanglement entropy characterizes the communication between two braneworld black holes, coupled to each other through a common bath. We find a Page curve consistent with unitarity. The gravitational result, computed using double-holographically realized quantum extremal surfaces, matches the conformal field theory calculation.At zero temperature, we obtain an interesting extension of the AdS3/BCFT2 correspondence. For a central charge c, we find a gap $$ \left(\frac{c}{16},\frac{c}{12}\right) $$ c 16 c 12 in the spectrum of the scaling dimension ∆bcc of the boundary condition changing operator (which interpolates mismatched boundary conditions on the two boundaries of the BCFT). Depending on the value of ∆bcc, the gravitational dual is either a defect global AdS3 geometry or a single sided black hole, and in both cases there are two Karch-Randall branes.

scholarly journals Two-point function of the energy-momentum tensor and generalised conformal structure

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Claudio Corianò ◽  
Luigi Delle Rose ◽  
Kostas Skenderis
Keyword(s):  
Gauge Theories ◽  
Energy Momentum Tensor ◽  
Conformal Structure ◽  
Momentum Tensor ◽  
Usual Sense ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Field ◽  
Multiplicative Factor ◽  
Dimensionless Coupling

AbstractTheories with generalised conformal structure contain a dimensionful parameter, which appears as an overall multiplicative factor in the action. Examples of such theories are gauge theories coupled to massless scalars and fermions with Yukawa interactions and quartic couplings for the scalars in spacetime dimensions other than 4. Many properties of such theories are similar to that of conformal field theories (CFT), and in particular their 2-point functions take the same form as in CFT but with the normalisation constant now replaced by a function of the effective dimensionless coupling g constructed from the dimensionful parameter and the distance separating the two operators. Such theories appear in holographic dualities involving non-conformal branes and this behaviour of the correlators has already been observed at strong coupling. Here we present a perturbative computation of the two-point function of the energy-momentum tensor to two loops in dimensions $$d= 3, 5$$ d = 3 , 5 , confirming the expected structure and determining the corresponding functions of g to this order, including the effects of renormalisation. We also discuss the $$\hbox {d}=4$$ d = 4 case for comparison. The results for $$d=3$$ d = 3 are relevant for holographic cosmology, and in this case we also study the effect of a $$\Phi ^6$$ Φ 6 coupling, which while marginal in the usual sense it is irrelevant from the perspective of the generalised conformal structure. Indeed, the effect of such coupling in the 2-point function is washed out in the IR but it modifies the UV.

scholarly journals Chaos and pole skipping in CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
David M. Ramirez
Keyword(s):  
Energy Density ◽  
Quantum Chaos ◽  
Central Charge ◽  
Finite Size ◽  
Complex Frequency ◽  
Conformal Field Theories ◽  
Point Function ◽  
Light Spectrum ◽  
Conformal Field ◽  
Stress Energy

Abstract Recent work has suggested an intriguing relation between quantum chaos and energy density correlations, known as pole skipping. We investigate this relationship in two dimensional conformal field theories on a finite size spatial circle by studying the thermal energy density retarded two-point function on a torus. We find that the location ω* = iλ of pole skipping in the complex frequency plane is determined by the central charge and the stress energy one-point function 〈T〉 on the torus. In addition, we find a bound on λ in c > 1 compact, unitary CFT2s identical to the chaos bound, λ ≤ 2πT. This bound is saturated in large c CFT2s with a sparse light spectrum, as quantified by [1], for all temperatures above the dual Hawking-Page transition temperature.

scholarly journals Recursion relations for 5-point conformal blocks

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
David Poland ◽  
Valentina Prilepina
Keyword(s):  
Linear Combination ◽  
Energy Operator ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Expectation Value ◽  
Conformal Field ◽  
Weight Shifting

Abstract We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

scholarly journals Hexagonalization of Fishnet integrals. Part I. Mirror excitations

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Enrico Olivucci
Keyword(s):  
Separation Of Variables ◽  
Bound State ◽  
Internal Symmetry ◽  
Irreducible Representations ◽  
Conformal Field Theories ◽  
Transfer Matrices ◽  
Conformal Field ◽  
State Index ◽  
Fixed Boundaries ◽  
Scaling Dimension

Abstract In this paper we consider a conformal invariant chain of L sites in the unitary irreducible representations of the group SO(1, 5). The k-th site of the chain is defined by a scaling dimension ∆k and spin numbers $$ \frac{\ell_k}{2},\frac{\ell_k}{2} $$ ℓ k 2 , ℓ k 2 The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice “fishnet” integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the mirror excitations of the lattice: particles with SO(4) internal symmetry that scatter according to an integrable factorized $$ \mathcal{S} $$ S -matrix in (1 + 1) dimensions

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

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