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I. Runkel

Publications and source records attributed to I. Runkel.

11 recordsLinked to original sources
arXiv2016

The non-semisimple Verlinde formula and pseudo-trace functions

We point out that results of Shimizu on internal characters imply a useful non-semisimple variant of the categorical Verlinde formula for factorisable finite tensor categories. When combined with results on pseudo-trace functions by Miyamoto and Arike-Nagatomo, one can make a precise conjecture for a non-semisimple modular Verlinde formula which relates modular properties of pseudo-trace functions and the product in the Grothendieck ring of the corresponding vertex operator algebra.

math.QA↗
arXiv2015

Symplectic fermions and a quasi-Hopf algebra structure on $\bar{U}_i sl(2)$

We consider the (finite-dimensional) small quantum group $\bar{U}_q sl(2)$ at $q=i$. We show that $\bar{U}_i sl(2)$ does not allow for an R-matrix, even though $U \otimes V \cong V \otimes U$ holds for all finite-dimensional representations $U,V$ of $\bar{U}_i sl(2)$. We then give an explicit coassociator $\Phi$ and an R-matrix $R$ such that $\bar{U}_i sl(2)$ becomes a quasi-triangular quasi-Hopf algebra. Our construction is motivated by the two-dimensional chiral conformal field theory of symplectic fermions with central charge $c=-2$. There, a braided monoidal category, $\mathcal{SF}$, has been computed from the factorisation and monodromy properties of conformal blocks, and we prove that $\mathrm{Rep}\,(\bar{U}_i sl(2),\Phi,R)$ is braided monoidally equivalent to $\mathcal{SF}$.

math.QA↗
arXiv2003

An algorithm for twisted fusion rules

We present an algorithm for an efficient calculation of the fusion rules of twisted representations of untwisted affine Lie algebras. These fusion rules appear in WZW orbifold theories and as annulus coefficients in boundary WZW theories; they provide NIM-reps of the WZW fusion rules.

math.QA↗
arXiv2003

Constructing Gauge Theory Geometries from Matrix Models

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

hep-th↗
arXiv2002

A non-rational CFT with central charge 1

Two dimensional conformal field theories with central charge one are discussed. After a short review of theories based on one free boson, a different CFT is described, which is obtained as a limit of minimal models.

hep-th↗
arXiv2001

Conformal Correlation Functions, Frobenius Algebras and Triangulations

We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories. The central ingredient is a special Frobenius algebra object A in the modular category that encodes the Moore-Seiberg data of the underlying chiral CFT. Just like for lattice TFTs, this algebra is itself not an observable quantity. Rather, Morita equivalent algebras give rise to equivalent theories. Morita equivalence also allows for a simple understanding of T-duality. We present a construction of correlators, based on a triangulation of the world sheet, that generalizes the one in lattice TFTs. These correlators are modular invariant and satisfy factorization rules. The construction works for arbitrary orientable world sheets, in particular for surfaces with boundary. Boundary conditions correspond to representations of the algebra A. The partition functions on the torus and on the annulus provide modular invariants and NIM-reps of the fusion rules, respectively.

hep-th↗
arXiv2001

A non-rational CFT with c=1 as a limit of minimal models

We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the free boson but bears some resemblance to Liouville theory. Explicit expressions for the three point functions of bulk fields are presented, as well as a set of conformal boundary states. We provide analytic and numerical arguments in support of the claim that this data forms a consistent CFT.

hep-th↗
arXiv2001

Minimal model boundary flows and c=1 CFT

We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation allows us to conjecture the IR limits of flows in the unitary minimal models generated by the fields ϕ_{rr} of `low' weight. We check this conjecture using the truncated conformal space approach. In the process we find evidence for a new series of integrable boundary flows.

hep-th↗
arXiv2000

Finite size effects in perturbed boundary conformal field theories

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.

hep-th↗
arXiv2000

Renormalisation group flows of boundary theories

We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR endpoints of certain flows, but also as a motivation for considering the particular limiting case of c = 1. By treating this limit, we are able to investigate a wide class of perturbations by considering them as deformations away from the c = 1 point. We also present the truncated conformal space approach as a tool for investigating the space of RG flows and checking particular predictions.

hep-th↗