Anatoly Konechny

Boundary entropy of one-dimensional quantum systems at low temperature.

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the ground-state degeneracy, g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.

Type 0 strings in a 2-d black hole

We study some aspects of type 0 strings propagating in the two dimensional black hole geometry, corresponding to the exact SL(2)/U(1) SCFT background.

On spectral density of Neumann matrices

Abstract In [L. Rastelli, et al., hep-th/0111281 ] the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at levelxa0L equals log L 2π . In this Letter we find an exact analytic expression for the finite part of the spectral density. This function allows one to calculate finite parts of various determinants arising in string field theory computations. We put our result to some consistency checks.

On the time-dependent description for the decay of unstable D-branes

We discuss how to describe time-dependent phenomena in string theory like the decay of unstable D-branes with the help of the world-sheet formulation. It is shown in a nontrivial well-controlled example that the coupling of the tachyons to propagating on-shell modes which escape to infinity can lead to time-dependent relaxation into a stationary final state. The final state corresponds to a fixed point of the RG flow generated by the relevant field from which the tachyon vertex operator is constructed. On the way we set up a fairly general formalism for the description of slow time-dependent phenomena with the help of conformal perturbation theory on the world-sheet.

The ground ring of N=2 minimal string theory

Abstract We study the N = 2 string theory or the N = 4 topological string on the deformed CHS background. That is, we consider the N = 2 minimal model coupled to the N = 2 Liouville theory. This model describes holographically the topological sector of little string theory. We use degenerate vectors of the respective N = 2 Verma modules to find the set of BRST cohomologies at ghost number zero—the ground ring, and exhibit its structure. Physical operators at ghost number one constitute a module of the ground ring, so the latter can be used to constrain the S-matrix of the theory. We also comment on the inequivalence of BRST cohomologies of the N = 2 string theory in different pictures.

On thermodynamical properties of some coset CFT backgrounds

We investigate the thermodynamical features of two lorentzian signature backgrounds that arise in string theory as exact CFTs and possess more than two disconnected asymptotic regions: the 2-d charged black hole and the Nappi-Witten cosmological model. We find multiple smooth disconnected euclidean versions of the charged black hole background. They are characterized by different temperatures and electro-chemical potentials. We show that there is no straightforward analog of the Hartle-Hawking state that would express these thermodynamical features. We also obtain multiple euclidean versions of the Nappi-Witten cosmological model and study their singularity structure. It suggests to associate a non-isotropic temperature with this background.

Infrared properties of boundaries in one-dimensional quantum systems

We present some partial results on the general infrared behaviour of bulk critical 1D quantum systems with a boundary. We investigate whether the boundary entropy, s(T ), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the infrared limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviours far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta function is the gradient of the boundary entropy, which implies that s(T )d ecreases with T.T he metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.

Ising model with a boundary magnetic field — an example of a boundary flow

In [1] a nonperturbative proof of the g-theorem of Affleck and Ludwig was put forward. In this paper we illustrate how the proof of [1] works on the example of the 2D Ising model at criticality perturbed by a boundary magnetic field. For this model we present explicit computations of all the quantities entering the proof including various contact terms. A free massless boson with a boundary mass term is considered as a warm-up example.

g-FUNCTION IN PERTURBATION THEORY

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

Noncommutative Tori, Yang–Mills, and String Theory

Noncommutative tori are among historically the oldest and by now the most developed examples of noncommutative spaces. Noncommutative Yang-Mills theory can be obtained from string theory. This connection led to a cross-fertilization of research in physics and mathematics on Yang-Mills theory on noncommutative tori. One important result stemming from that work is the link between T-duality in string theory and Morita equivalence of associative algebras. In this article we give an overview of the basic results in differential geometry of noncommutative tori. Yang-Mills theory on noncommutative tori, the duality induced by Morita equivalence and its link with the T-duality are discussed. Noncommutative Nahm transform for instantons is introduced.