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 On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals Quantum dimension as entanglement entropy in two dimensional conformal field theories

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
Song He ◽  
Tokiro Numasawa ◽  
Tadashi Takayanagi ◽  
Kento Watanabe
Keyword(s):  
Entanglement Entropy ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field

scholarly journals Logarithmic negativity in quantum Lifshitz theories

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
J. Angel-Ramelli ◽  
C. Berthiere ◽  
V. Giangreco M. Puletti ◽  
L. Thorlacius
Keyword(s):  
Entanglement Entropy ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Finite Part ◽  
Mixed States ◽  
Critical System ◽  
Conformal Field ◽  
Logarithmic Negativity ◽  
Spatial Dimensions

Abstract We investigate quantum entanglement in a non-relativistic critical system by calculating the logarithmic negativity of a class of mixed states in the quantum Lifshitz model in one and two spatial dimensions. In 1+1 dimensions we employ a correlator approach to obtain analytic results for both open and periodic biharmonic chains. In 2+1 dimensions we use a replica method and consider spherical and toroidal spatial manifolds. In all cases, the universal finite part of the logarithmic negativity vanishes for mixed states defined on two disjoint components. For mixed states defined on adjacent components, we find a non-trivial logarithmic negativity reminiscent of two-dimensional conformal field theories. As a byproduct of our calculations, we obtain exact results for the odd entanglement entropy in 2+1 dimensions.

THE ANNIHILATING IDEALS OF MINIMAL MODELS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 217-238 ◽  
Author(s):  
BORIS L. FEIGIN ◽  
TOMOKI NAKANISHI ◽  
HIROSI OOGURI
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Finite Models ◽  
Conformal Field ◽  
Intimate Relation ◽  
Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

scholarly journals Coset construction of Virasoro minimal models and coupling of Wess–Zumino–Witten theory with Schramm–Loewner evolution

2019 ◽  
Vol 31 (10) ◽  
pp. 1950037
Author(s):  
Shinji Koshida
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Loewner Evolution ◽  
Witten Theory ◽  
Coset Construction ◽  
New Perspective ◽  
Group Symmetries ◽  
Math Phys

Schramm–Loewner evolution (SLE) is a random process that gives a useful description of fractal curves. After its introduction, many works concerning the connection between SLE and conformal field theory (CFT) have been carried out. In this paper, we develop a new method of coupling SLE with a Wess–Zumino–Witten (WZW) model for [Formula: see text], an example of CFT, relying on a coset construction of Virasoro minimal models. Generalizations of SLE that correspond to WZW models were proposed by previous works [E. Bettelheim et al., Stochastic Loewner evolution for conformal field theories with Lie group symmetries, Phys. Rev. Lett. 95 (2005) 251601] and [Alekseev et al., On SLE martingales in boundary WZW models, Lett. Math. Phys. 97 (2011) 243–261], in which the parameters in the generalized SLE for [Formula: see text] were related to the level of the corresponding [Formula: see text]-WZW model. The present work unveils the mechanism of how the parameters were chosen, and gives a simpler proof of the result in these previous works, shedding light on a new perspective of SLE/WZW coupling.

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 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 On Fusion Rules in Logarithmic Conformal Field Theories

1997 ◽  
Vol 12 (10) ◽  
pp. 1943-1958 ◽  
Author(s):  
Michael A. I. Flohr
Keyword(s):  
Quantum Group ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Group Representations ◽  
Fusion Rules ◽  
Conformal Field ◽  
Almost All

We find the fusion rules for the cp,1 series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance of negative fusion coefficients which can be understood in terms of exceptional quantum group representations. The effective fusion rules (i.e. without signs and multiplicities) resemble the BPZ fusion rules for the virtual minimal models with conformal grid given via c = c3p,3. This leads to the conjecture that (almost) all minimal models with c = cp,q, gcd (p,q) > 1, belong to the class of rational logarithmic conformal field theories.

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