Rare Decay Modes of Quarter BPS Dyons

The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is known to jump across walls of marginal stability on which a quarter BPS dyon can decay into a pair of half BPS dyons. We show that as long as the electric and magnetic charges of the original dyon are primitive elements of the charge lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes marginally unstable against decay into a pair of quarter BPS dyons or a half BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any pair of generic points in the moduli space can be connected by a path avoiding these subspaces and there is no jump in the spectrum associated with these subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no change in the result

Quantum Entropy Function from AdS(2)/CFT(1) Correspondence

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, -- named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.Comment: LaTeX file, 27 pages, A modified and extended version of the talk given at Strings 200

Integration over a space of non-parametrized arcs, and motivic analogues of the monodromy zeta function

Notions of integration of motivic type over the space of arcs factorized by the natural C*-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on ℂd are given that correspond to these notions. Another key ingredient in the construction of these motivic versions of the zeta function is the use of the so-called power structure over the Grothendieck ring of varieties introduced by the authors

The Wave Function of Vasiliev's Universe - A Few Slices Thereof

We study the partition function of the free Sp(N) conformal field theory recently conjectured to be dual to asymptotically de Sitter higher-spin gravity in four-dimensions. We compute the partition function of this CFT on a round sphere as a function of a finite mass deformation, on a squashed sphere as a function of the squashing parameter, and on an S2xS1 geometry as a function of the relative size of S2 and S1. We find that the partition function is divergent at large negative mass in the first case, and for small $S^1$ in the third case. It is globally peaked at zero squashing in the second case. Through the duality this partition function contains information about the wave function of the universe. We show that the divergence at small S1 occurs also in Einstein gravity if certain complex solutions are included, but the divergence in the mass parameter is new. We suggest an interpretation for this divergence as indicating an instability of de Sitter space in higher spin gravity, consistent with general arguments that de Sitter space cannot be stable in quantum gravity.Comment: 30 pages plus appendices, 6 figure

Constructive Wall-Crossing and Seiberg-Witten

We outline a comprehensive and first-principle solution to the wall-crossing problem in D=4 N=2 Seiberg-Witten theories. We start with a brief review of the multi-centered nature of the typical BPS states and recall how the wall-crossing problem thus becomes really a bound state formation/dissociation problem. Low energy dynamics for arbitrary collections of dyons is derived, from Seiberg-Witten theory, with the proximity to the so-called marginal stability wall playing the role of the small expansion parameter. We find that, surprisingly, the $\mathbb{R}^{3n}$ low energy dynamics of n+1 BPS dyons cannot be consistently reduced to the classical moduli space, \CM, yet the index can be phrased in terms of \CM. We also explain how an equivariant version of this index computes the protected spin character of the underlying field theory, where SO(3)_\CJ isometry of \CM turns out to be the diagonal subgroup of $SU(2)_L$ spatial rotation and $SU(2)_R$ R-symmetry. The so-called rational invariants, previously seen in the Kontsevich-Soibelman formalism of wall-crossing, are shown to emerge naturally from the orbifolding projection due to Bose/Fermi statistics.Comment: 25 pages, conference proceeding contribution for "Progress of Quantum Field Theory and String Theory," Osaka, April 201

Black Hole Deconstruction

A D4-D0 black hole can be deconstructed into a bound state of D0 branes with a D6-anti-D6 pair containing worldvolume fluxes. The exact spacetime solution is known and resembles a D0 accretion disk surrounding a D6-anti-D6 core. We find a scaling limit in which the disk and core drop inside an AdS_2 throat. Crossing this AdS_2 throat and the D0 accretion disk into the core, we find a second scaling region describing the D6-anti-D6 pair. It is shown that the M-theory lift of this region is AdS_3 x S^2. Surprisingly, time translations in the far asymptotic region reduce to global, rather than Poincare, time translations in this core AdS_3. We further find that the quantum mechanical ground state degeneracy reproduces the Bekenstein-Hawking entropy-area law.Comment: 11 page

Symmetric Points in the Landscape as Cosmological Attractors

In the landscape, if there is to be any prospect of scientific prediction, it is crucial that there be states which are distinguished in some way. The obvious candidates are states which exhibit symmetries. Here we focus on states which exhibit discrete symmetries. Such states are rare, but one can speculate that they are cosmological attractors. We investigate the problem in model landscapes and cosmologies which capture some of the features of candidate flux landscapes. In non-supersymmetric theories we find no evidence that such states might be cosmologically favored. In supersymmetric theories, simple arguments suggest that states which exhibit $R$ symmetries might be. Our considerations lead us to raise questions about some popular models of eternal inflation.Comment: 27 pages, latex, minor typo correcte