Schwinger pair production in AdS2

We analyze the pair production of charged particles in two-dimensional Anti-de Sitter space (AdS_2) with a constant, uniform electric field. We compute the production rate both at a semi-classical level, viewing Schwinger pair production as a tunneling event, and at the full quantum level, by extracting the imaginary part of the one-loop amplitude. In contrast to the usual Schwinger pair production in flat space, pair production in AdS_2 requires a sufficiently large electric field E^2> M^2+1/4 in order to overcome the confining effect of the AdS geometry -- put in another way, the presence of an electric field E raises the Breitenlohner-Freedman bound to M^2 > -1/4 + E^2. For E greater than this threshold, the vacuum is unstable to production of charged pairs in the bulk. We expect our results to be helpful in constructing supersymmetric AdS_2 X S^2 perturbative string vacua, which enter in the near-horizon limit of extremal charged black holes. Although the generalized Breitenlohner-Freedman bound is obeyed in these cases, production of BPS particles at threshold is possible and relevant for AdS_2 fragmentation.Comment: 23 pages, 4 figures, v2:important revision, discussion of one-loop amplitude extended, several references adde

Automorphic forms: a physicist's survey

Motivated by issues in string theory and M-theory, we provide a pedestrian introduction to automorphic forms and theta series, emphasizing examples rather than generality.Comment: 22 pages, to appear in the Proceedings of Les Houches Winter School ``Frontiers in Number Theory, Physics and Geometry'', March 9-21, 2003; v2: minor changes and clarifications, section 3.5 on pure spinors has been rewritte

U-duality and D-brane Combinatorics

We investigate D-brane instanton contributions to R^4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutperle and Vanhove, we derive the non-perturbative O(e^{-1/\lambda}) corrections to R^4 couplings by a sequence of T-dualities, and interpret them as precise configurations of bound states of D-branes wrapping cycles of the compactification torus. Dp-branes explicitely appear as fluxes on D(p+2)-branes, and as gauge instantons on D(p+4)-branes. Specific rules for weighting these contributions are obtained, which should carry over to more general situations. Furthermore, it is shown that U-duality in D<=6 relates these D-brane configurations to O(e^{-1/\lambda^2}) instantons for which a geometric interpretation is still lacking.Comment: 17 pages, LaTeX2e, intro. shortened and minor typos corrected, final versio

Near-Extremal Correlators and Generalized Consistent Truncation for AdS_{4|7}\times S^{7|4}

We present conjectures for the space-time form and leading large N dependence of extremal and near-extremal correlation functions in the \N=8 superconformal Yang-Mills theory in d=3 as well as in the (0,2) superconformal theory in d=6, using their gravity duals with M-theory on $AdS_4\times \S^7$ and $AdS_7 \times \S^4$ respectively. As a key part of the conjectures, we argue that the bulk couplings associated with extremal and near-extremal field configurations in the corresponding $AdS_4$ and $AdS_7$ gauged supergravities vanish. The vanishing of these couplings constitutes a generalization of the property of consistent truncation of the Kaluza-Klein modes.Comment: 22 pages, 2 figure

High Energy Scattering on Distant Branes

We consider the elastic scattering of two open strings living on two D-branes separated by a distance $r$. We compute the high-energy behavior of the amplitude, to leading order in string coupling, as a function of the scattering angle $\phi$ and of the dimensionless parameter $v= r/(\pi\alpha^\prime\sqrt{s})$ with $\sqrt{s}$ the center-of-mass energy. The result exhibits an interesting phase diagram in the $(v,\phi)$ plane, with a transition at the production threshold for stretched strings at $v=1$. We also discuss some more general features of the open-string semiclassical world-sheets, and use T-duality to give a quantum tunneling interpretation of the exponential suppression at high-energy.Comment: JHEP class, 18 pages, 8 figure

On the short-distance structure of irrational non-commutative gauge theories

As shown by Hashimoto and Itzhaki in hep-th/9911057, the perturbative degrees of freedom of a non-commutative Yang-Mills theory (NCYM) on a torus are quasi-local only in a finite energy range. Outside that range one may resort to a Morita equivalent (or T-dual) description appropriate for that energy. In this note, we study NCYM on a non-commutative torus with an irrational deformation parameter $\theta$. In that case, an infinite tower of dual descriptions is generically needed in order to describe the UV regime. We construct a hierarchy of dual descriptions in terms of the continued fraction approximations of $\theta$. We encounter different descriptions depending on the level of the irrationality of $\theta$ and the amount of non-locality tolerated. The behavior turns out to be isomorphic to that found for the phase structure of the four-dimensional Villain $Z_N$ lattice gauge theories, which we revisit as a warm-up. At large 't Hooft coupling, using the AdS/CFT correspondance, we find that there are domains of the radial coordinate $U$ where no T-dual description makes the derivative expansion converge. The radial direction obtains multifractal characteristics near the boundary of AdS.Comment: 17 pages, 4 figures, uses JHEP.cl

Interactions for Winding Strings in Misner Space

We compute correlation functions of closed strings in Misner space, a big crunch big bang universe. We develop a general method for correlators with twist fields, which are relevant for the investigation on the condensation of winding tachyon. We propose to compute the correlation functions by performing an analytic continuation of the results in C/Z_N Euclidean orbifold. In particular, we obtain a finite result for a general four point function of twist fields, which might be important for the interpretation as the quartic term of the tachyon potential. Three point functions are read off through the factorization, which are consistent with the known results.Comment: 29 pages, no figure; typos corrected, references adde

Closed Strings in Misner Space: Stringy Fuzziness with a Twist

Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is the simplest tree-level solution of string theory with a cosmological singularity. We compute tree-level scattering amplitudes involving twisted states, using operator and current algebra techniques. We find that, due to zero-point quantum fluctuations of the excited modes, twisted strings with a large winding number $w$ are fuzzy on a scale $\sqrt{\log w}$, which can be much larger than the string scale. Wave functions are smeared by an operator $\exp(\Delta(\nu) \partial_+ \partial_-)$ reminiscent of the Moyal-product of non-commutative geometry, which, since $\Delta(\nu)$ is real, modulates the amplitude rather than the phase of the wave function, and is purely gravitational in its origin. We compute the scattering amplitude of two twisted states and one tachyon or graviton, and find a finite result. The scattering amplitude of two twisted and two untwisted states is found to diverge, due to the propagation of intermediate winding strings with vanishing boost momentum. The scattering amplitude of three twisted fields is computed by analytic continuation from three-point amplitudes of states with non-zero $p^+$ in the Nappi-Witten plane wave, and the non-locality of the three-point vertex is found to diverge for certain kinematical configurations. Our results for the three-point amplitudes allow in principle to compute, to leading order, the back-reaction on the metric due to a condensation of coherent winding strings.Comment: 29 pages, Latex2e, uses JHEP3.cls; v3: minor corrections, final version to appear in JCA