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Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a…

High Energy Physics - Theory · Physics 2007-05-23 David Brungs , Werner Nahm

In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…

High Energy Physics - Theory · Physics 2023-01-27 Christopher P. Herzog , Vladimir Schaub

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…

High Energy Physics - Theory · Physics 2007-05-23 J. Fuchs , A. N. Schellekens , C. Schweigert

Holomorphic modular bootstrap is an approach to classifying rational conformal field theories making use of the modular differential equations. In this paper we explore its flavored refinement. For a class of chiral algebras, we propose…

High Energy Physics - Theory · Physics 2025-05-07 Yiwen Pan , Chenxi Zeng

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply…

Quantum Algebra · Mathematics 2007-05-23 J. Fuchs , C. Schweigert

We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed…

High Energy Physics - Theory · Physics 2018-12-26 Tokiro Numasawa , Satoshi Yamaguchi

In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…

Mathematical Physics · Physics 2016-10-24 Andras Laszlo

We investigate sl(n) conformal Toda theory with maximally symmetric boundaries. There are two types of maximally symmetric boundary conditions, due to the existence of an order two automorphism of the W(n>2) algebra. In one of the two…

High Energy Physics - Theory · Physics 2011-09-12 Vladimir Fateev , Sylvain Ribault

We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…

High Energy Physics - Theory · Physics 2015-06-26 E. Abdalla , M. C. B. Abdalla , G. Sotkov , M. Stanishkov

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…

High Energy Physics - Theory · Physics 2016-09-06 S. Ferrara , C. Fronsdal

Using the representation theory of the subgroups SL_2(Z_p) 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…

High Energy Physics - Theory · Physics 2016-09-06 W. Eholzer

The $sl(2)$ minimal theories are labelled by a Lie algebra pair $(A,G)$ where $G$ is of $A$-$D$-$E$ type. For these theories on a cylinder we conjecture a complete set of conformal boundary conditions labelled by the nodes of the tensor…

High Energy Physics - Theory · Physics 2009-10-31 Roger E. Behrend , Paul A. Pearce , Jean-Bernard Zuber

The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…

High Energy Physics - Theory · Physics 2009-11-10 J"urgen Fuchs , Ingo Runkel , Christoph Schweigert

We present a new conformal algebra. It is Z2 x Z2 graded and generated by three N=1 superconformal algebras coupled to each other by nontrivial relations of parafermionic type. The representation theory and unitary models of the algebra are…

High Energy Physics - Theory · Physics 2009-01-23 Boris Noyvert

We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in…

Mathematical Physics · Physics 2026-01-12 Chris Elliott , Owen Gwilliam , Matteo Lotito

We consider the field theory of $N$ massless bosons which are free except for an interaction localized on the boundary of their 1+1 dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a…

High Energy Physics - Theory · Physics 2009-10-28 Ali Yegulalp

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the…

High Energy Physics - Theory · Physics 2009-10-28 P. Bowcock , E. Corrigan , R. H. Rietdijk

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

Rings and Algebras · Mathematics 2019-12-30 Yuri Bahturin , Alberto Elduque , Mikhail Kochetov

Many extended conformal algebras with one generator in addition to the Virasoro field as well as Casimir algebras have non-trivial outer automorphisms which enables one to impose `twisted' boundary conditions on the chiral fields. We study…

High Energy Physics - Theory · Physics 2009-10-22 A. Honecker

Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector space induced by a complex simple Lie algebra. The goal of…

Probability · Mathematics 2025-12-24 Baptiste Cerclé , Nathan Huguenin