Relating Gauge Theories via Gauge/Bethe Correspondence

In this note, we use techniques from integrable systems to study relations between gauge theories. The Gauge/Bethe correspondence, introduced by Nekrasov and Shatashvili, identifies the supersymmetric ground states of an N=(2,2) supersymmetric gauge theory in two dimensions with the Bethe states of a quantum integrable system. We make use of this correspondence to relate three different quiver gauge theories which correspond to three different formulations of the Bethe equations of an integrable spin chain called the tJ model.Comment: 30 pages, published in JHEP. LaTeX problem correcte

Dynamical Properties of one dimensional Mott Insulators

At low energies the charge sector of one dimensional Mott insulators can be described in terms of a quantum Sine-Gordon model. Using exact results derived from integrability it is possible to determine dynamical properties like the frequency dependent optical conductivity. We compare the exact results to perturbation theory and renormalisation group calculations. We also discuss the application of our results to experiments on quasi-1D organic conductors.Comment: 17 pages, 5 figures, to appear in the proceedings of the NATO ASI/EC summer school "New Theoretical Approaches to Strongly Correlated Systems" Newton Institute for Mathematical Sciences, Cambridge UK, April 200

Lifting asymptotic degeneracies with the Mirror TBA

We describe a qualitative feature of the AdS_5 x S^5 string spectrum which is not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced discrete symmetry in the asymptotic limit, whereby extra energy degeneracy enters the spectrum. We discuss how finite size corrections should lift this degeneracy, through both perturbative (Luscher) and non-perturbative approaches (the Mirror TBA), and illustrate this explicitly on two such asymptotically degenerate states.Comment: v3, 20 pages, 1 figure, 2 tables, as publishe

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte

Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points

Spinons and triplons in spatially anisotropic frustrated antiferromagnets

The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schr\"odinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triangular antiferromagnet Cs_2CuCl_4. The spectral features in such antiferromagnets can be attributed to two types of excitations: descendents of one-dimensional spinons of individual chains, and coherently propagating "triplon" bound states of spinon pairs. We argue that triplons are generic features of spatially anisotropic frustrated antiferromagnets, and arise because the bound spinon pair lowers its kinetic energy by propagating between chains.Comment: 16 pages, 6 figure

Twisted Bethe equations from a twisted S-matrix

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.Comment: 42 pages; v2: a new appendix on sl(2) grading, 2 additional references, and some minor changes; v3: improved Appendix D, additional references, and further minor changes, to appear in JHE

Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models

We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio

Exploring the mirror TBA

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.Comment: 69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published versio

From Luttinger to Fermi liquids in organic conductors

This chapter reviews the effects of interactions in quasi-one dimensional systems, such as the Bechgaard and Fabre salts, and in particular the Luttinger liquid physics. It discusses in details how transport measurements both d.c. and a.c. allow to probe such a physics. It also examine the dimensional crossover and deconfinement transition occurring between the one dimensional case and the higher dimensional one resulting from the hopping of electrons between chains in the quasi-one dimensional structure.Comment: To be published In the book "The Physics of Organic Conductors and Superconductors", Springer, 2007, ed. A. Lebe