On the fermionic quasi-particle interpretation in minimal models of conformal field theory (original) (raw)

Quasi-Particles, Conformal Field Theory, and q-Series

International Journal of Modern Physics B, 1993

We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are q-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities.

Form factors for quasi-particles inc= 1 conformal field theory

Journal of Physics A: Mathematical and General, 2000

The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c = 1. The charged quasi-particles in these theories have fractional charge and obey a form of fractional statistics. In this paper we study form factors, which are matrix elements of physical (conformal) operators, evaluated in a quasi-particle basis that is organized according to the rules of fractional exclusion statistics. Using the systematics of Jack polynomials, we derive selection rules for a special class of form factors. We argue that finite temperature Green's functions can be evaluated via systematic form factor expansions, using form factors such as those computed in this paper and thermodynamic distribution functions for fractional exclusion statistics. We present a specific case study where we demonstrate that the form factor expansion shows a rapid convergence.

On the application of conformal symmetry to quantum field theory

Physics Letters B

To leading order in ~xs(Q2), conformal symmetry specifies the eigensolutions of the evolution equation for meson distribution amplitudes, the wavefunctions which control large-momentum-transfer exclusive mesonic processes in QCD. We find that at next to leading order, the eigensolutions in various field theories depend on the regularization scheme, even for zero fl-function. This is contrary to the expectations of conformal symmetry.

Lectures on Conformal Field Theory

2002

in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions working toward current research topics in conformal field theory. We assume the reader to be familiar with quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help. These notes include over 80 homework problems and over 45 longer exercises for students.

March 1993 Introduction to Conformal Field Theory ∗

2009

In these lectures, we provide a introduction to Conformal Field Theory with applications to Condensed Matter Physics in mind. More directly, these provide the background information one would need for the lectures given by P. Durganandini in this Workshop. Hence these are not comprehensive. The interested reader is directed to some of the more elaborate reviews on the subject[3, 4].

The space of two dimensional quantum field theories: deformations of conformal models

The space of two dimensional quantum field theories: deformations of conformal models, 2022

In this thesis we study some deformations of conformal minimal models. In particular we study the imaginary magnetic deformation of the tricritical Ising model. The results and methodologies of this thesis are to be considered linked to what was known and discovered by the authors at the time of writing the thesis. There are errors (in the last chapter), then corrected in the paper: 2211.01123

Minimal Representations and Reductive Dual Pairs in Conformal Field Theory

2010

A minimal representation of a simple non-compact Lie group is obtained by "quantizing" the minimal nilpotent coadjoint orbit of its Lie algebra. It provides context for Roger Howe's notion of a reductive dual pair encountered recently in the description of global gauge symmetry of a (4-dimensional) conformal observable algebra. We give a pedagogical introduction to these notions and point out that physicists have been using both minimal representations and dual pairs without naming them and hence stand a chance to understand their theory and to profit from it.

Fermionic sum representations for conformal field theory characters

Physics Letters B, 1993

We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general (G (1) ) k ×(G (1) ) l (G (1) ) k+l coset conformal field theories, the non-unitary minimal models M(p, p + 2) and M(p, kp + 1), the N =2 superconformal series, and the Z N -parafermion theories, and relate the q → 1 behaviour of all these fermionic sum representations to the thermodynamic Bethe Ansatz.

Conformal field theories in a magnetic field

2024

We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs, for example, with a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge.