On the Central Charge of Spacetime Current Algebras and Correlators in String Theory on AdS3

Spacetime Virasoro and affine Lie algebras for strings propagating in AdS3 are known to all orders in $\alpha'$. The central extension of such algebras is a string vertex, whose expectation value can depend on the number of long strings present in the background but should be otherwise state-independent. In hep-th/0106004, on the other hand, a state-dependent expectation value was found. Another puzzling feature of the theory is lack of cluster decomposition property in certain connected correlators. This note shows that both problems can be removed by defining the free energy of the spacetime boundary conformal field theory as the Legendre transform of the formula proposed in the literature. This corresponds to pass from a canonical ensemble, where the number of fundamental strings that create the background can fluctuate, to a microcanonical one, where it is fixed.Comment: 10 pages, one minor correction, version published in JHE

String Phase Transitions in a Strong Magnetic Field

We consider open strings in an external constant magnetic field $H$. For an (infinite) sequence of critical values of $H$ an increasing number of (highest spin component) states lying on the first Regge trajectory becomes tachyonic. In the limit of infinite $H$ all these states are tachyons (with a common tachyonic mass) both in the case of the bosonic string and for the Neveu-Schwarz sector of the fermionic string. This result generalizes to extended object the same instability which occurs in ordinary non-Abelian gauge theories. The Ramond states have always positive square masses as is the case for ordinary QED. The weak field limit of the mass spectrum is the same as for a field theory with gyromagnetic ratio $g_S=2$ for all charged spin states. This behavior suggests a phase transition of the string as it has been argued for the ordinary electroweak theory.Comment: 8 page

Notes on a Cure for Higher-Spin Acausality

We present a Lagrangian describing a massive charged spin-2 field and a scalar in a constant electromagnetic background, and we provide a consistent description of the system. The Lagrangian, derived from string field theory through a suitable dimensional reduction, propagates the correct number of degrees of freedom within the light cone in any space-time dimension less than 26. We briefly discuss the higher-spin generalization of this construction, that cures the pathologies of a massive charged particle of arbitrary integer spin by introducing only finitely many new massive degrees of freedom.Comment: 14 pages, comments and references added, minor reorganization done. To appear in PR

On a Canonical Quantization of 3D Anti de Sitter Pure Gravity

We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,R) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS3.Comment: 61 pages, 7 figures. Minor misprints corrected, text in sections 1.3 and 5.4 clarified; version accepted for publication in JHEP. The first version was released jointly with arXiv:1508.04079 [hep-th

Ghosts of Critical Gravity

Recently proposed "critical" higher-derivative gravities in $AdS_D$ $D>3$ are expected to carry logarithmic representation of the Anti de Sitter isometry group. In this note, we quantize linear fluctuations of these critical gravities, which are known to be either identical with linear fluctuations of Einstein's gravity or else satisfy logarithmic boundary conditions at spacial infinity. We identify the scalar product uniquely defined by the symplectic structure implied by the classical action, and show that it does not posses null vectors. Instead, we show that the scalar product between any two Einstein modes vanishes, while the scalar product of an Einstein mode with a logarithmic mode is generically nonzero. This is the basic property of logarithmic representation that makes them neither unitary nor unitarizable.Comment: v2: typos corrected and slight clarifications. 11 page