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Related papers: K-matrices for 2D conformal field theories

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We study solutions of the Knizhnik-Zamolodchikov equation for discrete representations of SU(2)_k at rational level k+2=p/q using a regular basis in which the braid matrices are well defined for all spins. We show that at spin J=(j+1)p-1…

High Energy Physics - Theory · Physics 2011-02-16 A. Nichols

We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We…

High Energy Physics - Theory · Physics 2021-10-08 Kieran Finn , Sotirios Karamitsos , Apostolos Pilaftsis

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…

Mathematical Physics · Physics 2018-04-24 Yasuyuki Kawahigashi

We consider two types of quotients of the integrable modules of $\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants,…

Mathematical Physics · Physics 2007-05-23 B. Feigin , R. Kedem , S. Loktev , T. Miwa , E. Mukhin

We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT…

Mathematical Physics · Physics 2009-02-24 Liang Kong , Ingo Runkel

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in cond-mat/9912287 to the description of a quantum Hall fluid at non standard fillings nu=m/(pm+2). The chiral primary fields…

Condensed Matter · Physics 2009-10-31 G. Cristofano , G. Maiella , V. Marotta

We give the fermionic character formulas for the spaces of coinvariants obtained from level $k$ integrable representations of $\hat{\mathfrak sl}_2$. We establish the functional realization of the spaces dual to the coinvariant spaces. We…

Quantum Algebra · Mathematics 2007-05-23 B. Feigin , R. Kedem , S. Loktev , T. Miwa , E. Mukhin

Thus far in the search for, and classification of, `physical' modular invariant partition functions $\sum N_{LR}\,\c_L\,\C_R$ the attention has been focused on the {\it symmetric} case where the holomorphic and anti-holomorphic sectors, and…

High Energy Physics - Theory · Physics 2009-10-22 Terry Gannon

We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…

High Energy Physics - Theory · Physics 2024-09-20 Kohki Kawabata , Shinichiro Yahagi

In a recent paper Flohr, Grabow and Koehn conjectured that the characters of the logarithmic conformal field theory c_{k,1}, of central charge c=1-6(k-1)^2/k, admit fermionic representations labelled by the Lie algebra D_k. In this note we…

High Energy Physics - Theory · Physics 2008-11-26 S Ole Warnaar

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with…

High Energy Physics - Theory · Physics 2016-11-23 Timothy J. Hollowood , J. Luis Miramontes , David M. Schmidtt

The paper discusses the following topics: spinor coverings for the full Lorentz group, intrinsic parity of fermions, Majorana fermions, spinor structure of space models, two types of spacial spinors, parametrization of spinor spaces by…

Quantum Physics · Physics 2014-11-03 E. Ovsiyuk , O. Veko , A. Oana , M. Neagu , V. Balan , V. Red'kov

Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…

High Energy Physics - Theory · Physics 2007-05-23 Jürgen Fuchs , Ingo Runkel , Christoph Schweigert

The magic triangle due to Cvitanovi\'c and Deligne--Gross is an extension of the Freudenthal--Tits magic square of semisimple Lie algebras. In this paper, we identify all two-dimensional rational conformal field theories associated to the…

High Energy Physics - Theory · Physics 2026-04-20 Kimyeong Lee , Kaiwen Sun

We construct a Hochschild-Kostant-Rosenberg-type quasi-isomorphism for the negative cyclic homology of the category of global matrix factorizations on a smooth separated scheme of finite type over a field. The map is explicit enough to…

Algebraic Geometry · Mathematics 2021-09-30 Kuerak Chung , Bumsig Kim , Taejung Kim

Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…

Mathematical Physics · Physics 2014-11-18 I. T. Todorov

We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c<1 unitary…

High Energy Physics - Theory · Physics 2011-08-17 P. Bouwknegt , K. Schoutens

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…

High Energy Physics - Theory · Physics 2016-02-17 Daniel Friedan , Christoph A. Keller

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of…

High Energy Physics - Theory · Physics 2009-11-10 J. -F. Fortin , P. Jacob , P. Mathieu

In the old spirit of Kaluza-Klein, we consider a spacetime of the form $P = M_4 \times K$, where $K$ is the Lie group $\mathrm{SU}(3)$ equipped with a left-invariant metric that is not fully right-invariant. We observe that a complete…

High Energy Physics - Theory · Physics 2021-09-20 Joao Baptista