scholarly journals Gravity duals of quantum distances

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Run-Qiu Yang
Keyword(s):  
Field Theory ◽  
Ground State ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Trace Distance ◽  
Conformal Field ◽  
Holographic Approach ◽  
Rényi Relative Entropy ◽  
Bures Distance ◽  
Gravity Duals

Abstract This paper provides a holographic approach to compute some most-frequently used quantum distances and quasi-distances in strongly coupling systems and conformal field theories. By choosing modular ground state as the reference state, it finds that the trace distance, Fubini-Study distance, Bures distance and Rényi relative entropy, all have gravity duals. Their gravity duals have two equivalent descriptions: one is given by the integration of the area of a cosmic brane, the other one is given by the Euclidian on-shell action of dual theory and the area of the cosmic brane. It then applies these duals into the 2-dimensional conformal field theory as examples and finds the results match with the computations of field theory exactly.

scholarly journals MORE ABOUT ALL CURRENT-ALGEBRAIC ORBIFOLDS

2001 ◽  
Vol 16 (01) ◽  
pp. 97-162 ◽  
Author(s):  
M. B. HALPERN ◽  
J. E. WANG
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Ground State ◽  
Field Theories ◽  
Conformal Weight ◽  
Conformal Field Theories ◽  
Twisted Sector ◽  
Conformal Field ◽  
Adjoint Operation

Recently a construction was given for the stress tensors of all sectors of the general current-algebraic orbifold A(H)/H, where A(H) is any current-algebraic conformal field theory with a finite symmetry group H. Here we extend and further analyze this construction to obtain the mode formulation of each sector of each orbifold A(H)/H, including the twisted current algebra, the Virasoro generators, the orbifold adjoint operation and the commutator of the Virasoro generators with the modes of the twisted currents. As applications, general expressions are obtained for the twisted current–current correlator and ground state conformal weight of each twisted sector of any permutation orbifold A(H)/H, H⊂SN. Systematics are also outlined for the orbifolds A(Lie h(H))/H of the (H and Lie h)-invariant conformal field theories, which include the general WZW orbifold and the general coset orbifold. Finally, two new large examples are worked out in further detail: the general SNpermutation orbifold A(SN)/SNand the general inner-automorphic orbifold A(H(d))/H(d).

scholarly journals Gravity Duals for Nonrelativistic Conformal Field Theories

2008 ◽  
Vol 101 (6) ◽  
Author(s):  
Koushik Balasubramanian ◽  
John McGreevy
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Gravity Duals

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 GRAVITY DUAL FOR REGGEON FIELD THEORY AND NONLINEAR QUANTUM FINANCE

2009 ◽  
Vol 24 (32) ◽  
pp. 6197-6222 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Conformal Invariance ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Invariant ◽  
Galilean Invariance ◽  
Scale Invariant ◽  
Conformal Field ◽  
Nonlinear Quantum ◽  
Reggeon Field Theory

We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.

scholarly journals BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4497-4591 ◽  
Author(s):  
MICHAEL A. I. FLOHR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Hall ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Verlinde Formula

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

SOME LANDAU-GINZBURG MODELS FROM CONFORMAL FIELD THEORY

1990 ◽  
Vol 05 (12) ◽  
pp. 2343-2358 ◽  
Author(s):  
KEKE LI
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Operator Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Coset Models ◽  
Marginal Deformation

A method of constructing critical (fixed point) Landau-Ginzburg action from operator algebra is applied to several classes of conformal field theories, including lines of c = 1 models and the coset models based on SU(2) current algebra. For the c = 1 models, the Landau-Ginzberg potential is argued to be physically consistent, and it resembles a modality-one singularity with modal deformation representing exactly the marginal deformation. The potentials for the coset models manifestly possess correct discrete symmetries.

scholarly journals TWO-DIMENSIONAL FRACTIONAL SUPERSYMMETRIC CONFORMAL FIELD THEORIES AND THE TWO-POINT FUNCTIONS

2001 ◽  
Vol 16 (12) ◽  
pp. 2165-2173 ◽  
Author(s):  
FARDIN KHEIRANDISH ◽  
MOHAMMAD KHORRAMI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Closed Subalgebra

A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by (L-1,L0,G-1/3) and [Formula: see text], the two-point functions of the component fields of supermultiplets are calculated.

scholarly journals CHARACTERS FOR COSET CONFORMAL FIELD THEORIES AND MAVERICK EXAMPLES

1993 ◽  
Vol 08 (23) ◽  
pp. 4103-4121 ◽  
Author(s):  
DAVID C. DUNBAR ◽  
KEITH G. JOSHI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Current Method ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

We present an example of a coset conformal field theory which cannot be described by the identification current method. To study such examples we determine formulae for the characters of coset conformal field theories.

scholarly journals Logarithmic Operators in Conformal Field Theory and the ${\mathcal W}_\infty$-Algebra

1997 ◽  
Vol 12 (21) ◽  
pp. 3723-3738 ◽  
Author(s):  
A. Shafiekhani ◽  
M. R. Rahimi Tabar
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Tensor Operator ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation

It is shown explicitly that the correlation functions of conformal field theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of [Formula: see text]-algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary [Formula: see text]. This method allows us to write differential equations which can be used to find general expression for three- and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.

scholarly journals OPERATOR PRODUCT EXPANSION IN SL(2) CONFORMAL FIELD THEORY

2002 ◽  
Vol 17 (11) ◽  
pp. 683-693 ◽  
Author(s):  
KAZUO HOSOMICHI ◽  
YUJI SATOH
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Highest Weight ◽  
Wznw Model ◽  
Highest Weight Representations ◽  
Highest Weight Representation

In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL (2,R) WZNW model.

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