Quantization and Scattering in the IIB SL(2,Z) Covariant Superstring

We rewrite the SL(2,Z) covariant worldsheet action for the IIB string proposed by Townsend in a Polyakov form. In a flat background the formalism yields separate (p,q) sectors. In each one the action is that of the IIB string action with the string slope parameter \alp\pr replaced by its SL(2,Z) analogue \alp_{pq}\pr. SL(2,Z) invariant graviton scattering amplitudes are obtained from those of the fundamental (1,0) string by summing over the different sectors. The tree-level four-graviton amplitude in this formalism differs from a previously conjectured non-perturbative form; both yield the same expansion in order \alpha\pr^3.Comment: 15 pages, LaTeX, additional comment

Hydrodynamic charge and heat transport on inhomogeneous curved spaces

We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects, and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential, and discuss the extent to which our hydrodynamic theory is relevant for experimentally realizable condensed matter systems, including suspended graphene at the Dirac point.Comment: 15+8 pages, 4+1 figures; v2: added references, published versio

Pairing induced superconductivity in holography

We study pairing induced superconductivity in large $N$ strongly coupled systems at finite density using holography. In the weakly coupled dual gravitational theory the mechanism is conventional BCS theory. An IR hard wall cut-off is included to ensure that we can controllably address the dynamics of a single confined Fermi surface. We address in detail the interplay between the scalar order parameter field and fermion pairing. Adding an explicitly dynamical scalar operator with the same quantum numbers as the fermion-pair, the theory experiences a BCS/BEC crossover controlled by the relative scaling dimensions. We find the novel result that this BCS/BEC crossover exposes resonances in the canonical expectation value of the scalar operator. This occurs not only when the scaling dimension is degenerate with the Cooper pair, but also with that of higher derivative paired operators. We speculate that a proper definition of the order parameter which takes mixing with these operators into account stays finite nevertheless.Comment: 38 pages; 24 figures; revtex4 v2: Acknowledgements adde

Crosscaps in Gepner Models and the Moduli space of T2 Orientifolds

We study T^2 orientifolds and their moduli space in detail. Geometrical insight into the involutive automorphisms of T^2 allows a straightforward derivation of the moduli space of orientifolded T^2s. Using c=3 Gepner models, we compare the explicit worldsheet sigma model of an orientifolded T^2 compactification with the CFT results. In doing so, we derive half-supersymmetry preserving crosscap coefficients for generic unoriented Gepner models using simple current techniques to construct the charges and tensions of Calabi-Yau orientifold planes. For T^2s we are able to identify the O-plane charge directly as the number of fixed points of the involution; this number plays an important role throughout our analysis. At several points we make connections with the mathematical literature on real elliptic curves. We conclude with a preliminary extension of these results to elliptically fibered K3s.Comment: LaTeX, 59 pages, 21 figures (uses axodraw

Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for nonlinear sigma models

We write general one-loop anomalies of string field theory as path integrals on a torus for the corresponding nonlinear sigma model. This extends the work of Alvarez-Gaum\'e and Witten from quantum mechanics to two dimensions. Higher world-volume loops contribute in general to nontopological anomalies and a formalism to compute these is developed. We claim that (i) for general anomalies one should not use the propagator widely used in string theory but rather the one obtained by generalization from quantum mechanics, but (ii) for chiral anomalies both propagators give the same result. As a check of this claim in a simpler model we compute trace anomalies in quantum mechanics. The propagator with a center-of-mass zero mode indeed does not give the correct result for the trace anomaly while the propagator for fluctuations $q^i (\tau)$ satisfying $q^i (\tau = -1) = q^i (\tau = 0) = 0$ yields in $d=2$ and $d=4$ dimensions the correct results from two- and three-loop graphs. We then return to heterotic string theory and calculate the contributions to the anomaly from the different spin structures for $d=2$. We obtain agreement with the work of Pilch, Schellekens and Warner and that of Li in the sector with spacetime fermions. In the other sectors, where no explicit computations have been performed in the past and for which one needs higher loops, we find a genuine divergence, whose interpretation is unclear to us. We discuss whether or not this leads to a new anomaly.Comment: Latex, 32 pages, 4 fi

A note on four-point functions of conformal operators in N=4 Super-Yang Mills

We find that the first-order correction to the free-field result for the four-point function of the conformal operator \tr(\phi^i\phi^j) is nonvanishing and survives in the limit N_c \rar \infty.Comment: 4 pages, 7 eps-figs, LaTeX. Typos corrected, refs adde

Holographic dual of a time machine

We apply the $AdS/CFT$ holography to the simplest possible eternal time machine solution in $AdS_3$ based on two conical defects moving around their center of mass along a circular orbit. Closed timelike curves in this space-time extend all the way to the boundary of $AdS_3$, violating causality of the boundary field theory. By use of the geodesic approximation we address the "grandfather paradox" in the dual $1+1$ dimensional field theory and calculate the two-point retarded Green function. It has a non-trivial analytical structure both at negative and positive times, providing us with an intuition on how an interacting quantum field could behave once causality is broken. In contrast with the previous considerations our calculations reveal the possibility of a consistent and controllable evolution of a quantum system without any need to impose additional consistency constraints.Comment: 37 pages, 26 figure

Absence of disorder-driven metal-insulator transitions in simple holographic models

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to Einstein-Maxwell theory in an asymptotically $\mathrm{AdS}_4$ spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond non-perturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.Comment: 6 pages. v2: more references, minor changes. v3: published versio