Perturbative 4D conformal field theories and representation theory of diagram algebras

Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

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Holomorphic modular bootstrap revisited

Journal of High Energy Physics ◽

10.1007/jhep12(2021)151 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Justin Kaidi ◽

Ying-Hsuan Lin ◽

Julio Parra-Martinez

Keyword(s):

Differential Equations ◽

Representation Theory ◽

Field Theories ◽

Conformal Field Theories ◽

Conformal Field

Abstract In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, ℤn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

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Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block

Modern Physics Letters A ◽

10.1142/s0217732321502722 ◽

2021 ◽

Vol 36 (39) ◽

Author(s):

Yu Nakayama

Keyword(s):

Representation Theory ◽

Hypergeometric Function ◽

Conformal Block ◽

Field Theories ◽

Gauss Hypergeometric Function ◽

Conformal Field Theories ◽

Recursive Structure ◽

Conformal Blocks ◽

Conformal Field ◽

Pole Structure

The Gauß hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gauß hypergeometric function is slightly “off-shell”.

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Defects and perturbation

Journal of High Energy Physics ◽

10.1007/jhep04(2021)300 ◽

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.

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Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

Physical Review Research ◽

10.1103/physrevresearch.3.013248 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Hugo A. Camargo ◽

Lucas Hackl ◽

Michal P. Heller ◽

Alexander Jahn ◽

Tadashi Takayanagi ◽

...

Keyword(s):

Field Theories ◽

Conformal Field Theories ◽

Conformal Field

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NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x00002354 ◽

2000 ◽

Vol 15 (30) ◽

pp. 4857-4870 ◽

Cited By ~ 9

Author(s):

D. C. CABRA ◽

E. FRADKIN ◽

G. L. ROSSINI ◽

F. A. SCHAPOSNIK

Keyword(s):

Quantum Hall ◽

Field Theories ◽

Simons Theory ◽

Conformal Field Theories ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Conformal Field ◽

Quantum Hall States ◽

Effective Lagrangian ◽

Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

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Constructing Carrollian CFTs

Journal of High Energy Physics ◽

10.1007/jhep03(2021)194 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Nishant Gupta ◽

Nemani V. Suryanarayana

Keyword(s):

Scalar Fields ◽

Higher Dimensions ◽

Field Theories ◽

Conformal Field Theories ◽

Relativistic Limit ◽

Conformal Field ◽

Local Symmetries ◽

Derivatives Of ◽

Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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