Coset CFT Research Articles

Thermodynamical properties of some coset CFT backgrounds

AbstractWe 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 find 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.

D-branes on a gauged WZW model

The algebraic classification of Cardy for boundary states on a G/ H coset CFT of a compact group G, is geometrically realized on the corresponding manifold resulting from gauging the WZW model. The branes consist of H orbits of quantized G conjugacy classes shifted by quantized H conjugacy classes.

Superstring theory on AdS3 × G/H and boundary N = 3 superconformal symmetry

Superstrings propagating on backgrounds of the form AdS_3 x G/H are studied using the coset CFT approach. We focus on seven dimensional cosets which have a semiclassical limit, and which give rise to N=3 superconformal symmetry in the dual CFT. This is realized for the two cases AdS_3 x SU(3)/U(1) and AdS_3 x SO(5)/SO(3), for which we present an explicit construction. We also provide sufficient conditions on a CFT background to enable a similar construction, and comment on the geometrical interpretation of our results.

THE TWO-DIMENSIONAL STRINGY BLACK HOLE: A NEW APPROACH AND A NEW EFFECT

The string propagation in the two-dimensional stringy black hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the Lorentzian and Euclidean regimes. In the Lorentzian case all the physics reduces to a massless scalar particle described by a Klein-Gordon type equation with a singular effective potential. The scattering matrix is found and it reproduces the results obtained by coset CFT techniques. It factorizes into two pieces: an elastic Coulombian amplitude and an absorption part. In both parts, an infinite sequence of imaginary poles in the energy appears. The generic features of string propagation in curved D-dimensional backgrounds (string stretching, fall into space-time singularities) are analyzed in the present case. A new physical phenomenon specific to the present black hole is found: the quantum renormalization of the speed of light. We find that [Formula: see text] where k is the integer in front of the WZW action. Only for k→∞ does this new effect disappear (although the conformal anomaly is present). We analyze all the classical Euclidean string solutions and exactly compute the quantum partition function. No critical Hagedorn temperature appears here.

Four-dimensional plane wave string solutions with coset CFT description

We present a number of D = 4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by ‘boosting’ the twisted products of two D = 2 ‘cosmological’ or ‘black-hole’ cosets related to (G ⊗ G′)/(H ⊗ H′) (G, G′ = SL(2, R) or SU(2); H, H ′ = SO(1, 1) or SO(2)) gauged WZW models. We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with known string backgrounds. By applying a non-abelian duality transformation to the NW model we find a D = 4 solution which admits a covariantly constant null Killing vector but is not a plane wave. Higher dimensional bosonic backgrounds with isometries can be interpreted as lower dimensional ones with extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents also a D = 3 gravi-electromagnetic heterotic string plane wave. In addition to the (1, 1) supersymmetric embeddings of bosonic solutions we construct a number of non-trivial (1, 0) supersymmetric exact D = 4 heterotic string plane wave solutions some of which are related (by a boost and analytic continuation) to limiting cases of D = 4 heterotic black hole solutions.

Complete S-matrices of supersymmetric sine-gordon theory and perturbed superconformal minimal model

We derive the first complete S-matrices of the supersymmetric sine-Gordon theory for a general value of coupling constant. The spectrum includes not only solitons and antisolitons but also their bound states. The S-matrices are computed based on the soliton S-matrix which was obtained from the S-matrix of perturbed superconformal unitary model. After constructing a superconformal non-unitary model from the coset CFT with admissible representations, we derive the S-matrices of the perturbed superconformal non-unitary model by restricting the SSG S-matrices. We generalize these results to the theories with the fractional supersymmetries.

BRST cohomology and highest weight vectors. I

We initiate a program to study certain recent problems in non-compact coset CFT by the BRST approach. We derive a reduction formula for the BRST cohomology by making use of a twisting by highest weight modules. As illustrations, we apply the formula to the bosonic string model and a rank one non-compact coset model [DPL]. Our formula provides a completely new approach to non-compact coset construction.