Unitarity of supersymmetric SL(2,R)/U(1) and no-ghost theorem for fermionic strings in AdS(3) x N

The unitarity of the NS supersymmetric coset SL(2,R)/U(1) is studied for the discrete representations. The results are applied to the proof of the no-ghost theorem for fermionic strings in AdS(3) x N in the NS sector. A no-ghost theorem is proved for states in flowed discrete representations.Comment: LaTeX in JHEP style, 16 pages, typos correcte

Bayesian spike inference from calcium imaging data

We present efficient Bayesian methods for extracting neuronal spiking information from calcium imaging data. The goal of our methods is to sample from the posterior distribution of spike trains and model parameters (baseline concentration, spike amplitude etc) given noisy calcium imaging data. We present discrete time algorithms where we sample the existence of a spike at each time bin using Gibbs methods, as well as continuous time algorithms where we sample over the number of spikes and their locations at an arbitrary resolution using Metropolis-Hastings methods for point processes. We provide Rao-Blackwellized extensions that (i) marginalize over several model parameters and (ii) provide smooth estimates of the marginal spike posterior distribution in continuous time. Our methods serve as complements to standard point estimates and allow for quantification of uncertainty in estimating the underlying spike train and model parameters

The partition function of the supersymmetric two-dimensional black hole and little string theory

We compute the partition function of the supersymmetric two-dimensional Euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N=2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N=2 minimal model factor of the correct central charge and projecting on integral N=2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry.Comment: JHEP class, 35 pages, no figures; v2: minor changes, typos corrected, published versio

Extended SL(2,R)/U(1) characters, or modular properties of a simple non-rational conformal field theory

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N=2 algebras, we show that they have nice modular transformation properties. We calculate the modular matrices of this simple but non-trivial non-rational conformal field theory explicitly . As a result, we show that discrete SL(2,R) representations mix with continuous SL(2,R) representations under modular transformations in the coset conformal field theory. We comment upon the significance of our results for a general theory of non-rational conformal field theories.Comment: JHEP style, 25 pages, 2 figures, v2: minor corrections, reference added, version to appear in JHE

Spectral Flow in AdS(3)/CFT(2)

We study the spectral flowed sectors of the H3 WZW model in the context of the holographic duality between type IIB string theory in AdS(3)x S^3 x T^4 with NSNS flux and the symmetric product orbifold of T^4. We construct explicitly the physical vertex operators in the flowed sectors that belong to short representations of the superalgebra, thus completing the bulk-to-boundary dictionary for 1/2 BPS states. We perform a partial calculation of the string three-point functions of these operators. A complete calculation would require the three-point couplings of non-extremal flowed operators in the H3 WZW model, which are at present unavailable. In the unflowed sector, perfect agreement has recently been found between the bulk and boundary three-point functions of 1/2 BPS operators. Assuming that this agreement persists in the flowed sectors, we determine certain unknown three-point couplings in the H3 WZW model in terms of three-point couplings of affine descendants in the SU(2) WZW model.Comment: 50 pages, 2 figure

FZZ Scattering

We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is dual to itself under the interchange of the Liouville parameter b by 1/b. In both cases, a classical scattering problem does not determine uniquely the quantum reflection coefficient. The latter is only fixed by assuming that the dual scattering problem has the same reflection coefficient. We also discuss the relation of this approach to the method that exploits the parafermionic symmetry of the model to compute the reflection coefficient.Comment: 19 pages, JHEP style. v2: Minor changes in the proposed field of sine-Liouville type, new section discussing the relation with parafermionic symmetry, references adde

S-matrix for magnons in the D1-D5 system

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 $\times$ S3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.Comment: 40 pages, Latex, Role of Virasoro constraints clarified, version matches with published versio