Boundary sine-Gordon Theory Research Articles

Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature

The material copper pyrimidine dinitrate (Cu-PM) is a quasi-one-dimensional spin system described by the spin-1/2 XXZ Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. Based on numerical results obtained by the density-matrix renormalization group, exact diagonalization, and accompanying electron spin resonance (ESR) experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the low-energy description by the quantum sine-Gordon model. We find a deviation from the Lorentz invariant dispersion for the single-soliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sine-Gordon field theory, while composite boundary-bulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperature-induced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on Cu-PM over a wide range of the applied field.

Breather boundary form factors in sine-Gordon theory

A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by analytic continuation to sinh-Gordon model. We find that the numerical data strongly support the validity of the form factors themselves; however, we also report a discrepancy in the case of diagonal matrix elements, which remains unresolved for the time being.

Giant magnons and non-maximal giant gravitons

We produce the open strings on $\mathbb{R}\times S^{2}$ that correspond to the solutions of integrable boundary sine-Gordon theory by making use of the $N$-magnon solutions provided in \cite{KPV} together with explicit moduli. Relating the two boundary parameters in a special way we describe the scattering of giant magnons with non-maximal $Y=0$ giant gravitons and calculate the leading contribution to the associated magnon scattering phase.

Timelike boundary sine-Gordon theory and two-component plasma

It has long been known that there is a relation between boundary sine-Gordon theory and thermodynamics of charge neutral two-component Coulomb plasma on a unit circle. On the other hand, recently it was found that open string world sheet description of brane decay can be related to a sequence of points of thermodynamic equilibrium of one-component plasma. Here we consider a different decay process which is specifically described by the timelike boundary sine-Gordon theory. We find time evolution to be mapped to a one-dimensional curve in the space of points of thermal equilibrium of a non-neutral two-component Coulomb plasma. We compute the free energy of the system and find that along the curve it is monotonically decreasing, defining a thermodynamic arrow of time.

Boundary Liouville theory atc= 1

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models. Here we extend the analysis of the c=1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c=1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c=1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c=1 theory.

Finite size effects in boundary sine-Gordon theory

We examine the finite volume spectrum and boundary energy in boundary sine-Gordon theory, based on our recent results obtained by closing the boundary bootstrap. The spectrum and the reflection factors are checked against truncated conformal space, together with a (still unpublished) prediction by Al.B. Zamolodchikov for the boundary energy and the relation between the parameters of the scattering amplitudes and of the perturbed CFT Hamiltonian. In addition, a derivation of Zamolodchikov's formulae is given. We find an entirely consistent picture and strong evidence for the validity of the conjectured spectrum and scattering amplitudes, which together give a complete description of the boundary sine-Gordon theory on mass shell.

Thermodynamic Properties of the One-Dimensional Two-Component Log-Gas

We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full thermodynamics (density-fugacity relationship, specific heat, etc.) of the log-gas in the whole stability range of inverse temperatures β<1. An exact formula for the excess chemical potential of a “foreign” particle of an arbitrary charge, put into the log-gas, is derived. The results are checked by a small-β expansion and at the collapse β=1 point. The possibility to go beyond the collapse temperature is discussed.

Minimal models with integrable local defects

We describe a general way of constructing integrable defect theories as perturbations of conformal field theory by local defect operators. The method relies on folding the system onto a boundary field theory of twice the central charge. The classification of integrable defect theories obtained in this way parallels that of integrable bulk theories which are a perturbation of the tensor product of two conformal field theories. These include local defect perturbations of all c < 1 minimal models, as well as of the coset theories based on SO(2 n), obtained in this way. We discuss in detail the former case of all the Virasoro minimal models. In the Ising case our construction corresponds to having a spin field as a defect operator; in the folded formulation this is mapped onto an orbifolding of the boundary sine-Gordon theory at β 2/8π = 1 8 , or a version of the anisotropic Kondo model.

The Continuum Limit of the Integrable Open XYZ Spin-1/2 Chain

We show that the continuum limit of the integrable XYZ spin-1/2 chain on a half-line gives rise to the boundary sine-Gordon theory using the perturbation method.

The boundary sine-Gordon theory: Classical and semi-classical analysis

We consider the sine-Gordon model on a half-line, with an additional potential term of the form −M cos[ 1 2 β(ϕ − ϕ 0)] at the boundary. We compute the classical time delay for general values of M, β and ϕ 0 using τ-function methods and show that in the classical limit the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find agreement with the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.