Rational conformal field theory with matrix level and strings on a torus

Nassar, Ali; Walton, Mark A.
January 2014
Canadian Journal of Physics;Jan2014, Vol. 92 Issue 1, p65
Academic Journal
Study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes it obvious that the rational theories are dense in the moduli space of strings on T m, and may prove useful in other ways.


Related Articles

  • Left-right entanglement entropy of D p-branes. Zayas, Leopoldo; Quiroz, Norma // Journal of High Energy Physics;Nov2016, Vol. 2016 Issue 11, p1 

    We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density...

  • SO(N) restricted Schur polynomials. Kemp, Garreth // Journal of Mathematical Physics;2015, Vol. 56 Issue 2, p1 

    We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory...

  • Multi-matrix models and genus one amplitudes. Spodyneiko, L. // JETP Letters;Mar2014, Vol. 99 Issue 1, p47 

    The genus one correlation numbers in the matrix models and the minimal Liouville gravity have been studied. The torus partition function for the matrix models, as well as the one- and two-point correlation numbers of the (3, p) matrix models and (3, p) minimal Liouville gravity, has been calculated.

  • Topological defects in CFT. Petkova, V. // Physics of Atomic Nuclei;Oct2013, Vol. 76 Issue 10, p1268 

    Areview of the notion, properties and the use of topological defects in 2d conformal field theories is presented. An emphasis is made on the recent interpretation of such operators in non-rational theories, as describing Wilson-'t Hooft loop operators of N = 2 supersymmetric 4d topological theories.

  • Rationality of Bershadsky-Polyakov Vertex Algebras. Arakawa, Tomoyuki // Communications in Mathematical Physics;Oct2013, Vol. 323 Issue 2, p627 

    We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras $${W_3^{(2)}}$$ at level k = p/2−3 with $${p = 3, 5, 7, 9, \dots}$$ . This gives new examples of rational conformal...

  • Remarks on the Hall Conductivity in Chiral Superconductors: Weak vs. Strong Coupling Approach. ROGATKO, M.; WYSOKIŃSKI, K. I. // Acta Physica Polonica, A.;2014, Vol. 126 Issue 4a, pA-9 

    We discuss the calculations of the ac Hall conductivity for superconductors with the time reversal symmetry breaking states. In the weak coupling theories these states show vanishing Hall response in one band models, even though one expects otherwise on symmetry grounds. On the other hand, the...

  • Three-field potential for soft-wall AdS/QCD. Bartz, Sean P.; Kapusta, Joseph I. // AIP Conference Proceedings;Oct2013, Vol. 1560 Issue 1, p456 

    The Anti-de Sitter Space/Conformal Field Theory (AdS/CFT) correspondence may offer new and useful insights into the non-perturbative regime of strongly coupled gauge theories such as Quantum Chromodynamics (QCD). Soft-wall AdS/QCD models have reproduced the linear Regge trajectories of meson...

  • Entropy and Quantum Gravity. Kay, Bernard S. // Entropy;Dec2015, Vol. 17 Issue 12, p8174 

    We give a review, in the style of an essay, of the author's 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach...

  • Conformal Killing 2-forms on four-dimensional manifolds. Andrada, Adrián; Barberis, María; Moroianu, Andrei // Annals of Global Analysis & Geometry;Dec2016, Vol. 50 Issue 4, p381 

    We study four-dimensional simply connected Lie groups G with a left invariant Riemannian metric g admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action, or the metric is half-conformally flat. In the first...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics