We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U (1) gauge field with gauge coupling g, there is a new ultraviolet scale Λ = gM Pl , invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Λ. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light "elementary" electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.

Recently, Berenstein et al. have proposed a duality between a sector of N = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be λWe study Yang-Mills theory at small λ ′ (large µ) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g4 , the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g 2 √ λ ′ as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g 2 2 and λ ′ and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.

We argue that two four-dimensional strongly coupled superconformal field theories, on the Higgs branch in certain large N limits, become respectively (2, 0) theory and (1, 1) little string theory in six dimensions. We identify the spectrum of states responsible for the generation of the two extra dimensions and string winding modes. We establish the equivalence using orbifold realizations of the field theories and exploiting string dualities. We also speculate on deconstructions of M-theory.

We investigate the hypothesis that the higher-derivative corrections always make extremal non-supersymmetric black holes lighter than the classical bound and self-repulsive. This hypothesis was recently formulated in the context of the socalled swampland program. One of our examples involves an extremal heterotic black hole in four dimensions. We also calculate the effect of general four-derivative terms in Maxwell-Einstein theories in D dimensions. The results are consistent with the conjecture.

Abstract:We show that a subgroup of the modular group of M-theory compactified on a ten torus, implies the Lorentzian structure of the moduli space, that is usually associated with naive discussions of quantum cosmology based on the low energy Einstein action. This structure implies a natural division of the asymptotic domains of the moduli space into regions which can/cannot be mapped to Type II string theory or 11D Supergravity (SUGRA) with large radii. We call these the safe and unsafe domains. The safe domain is the interior of the future light cone in the moduli space while the unsafe domain contains the spacelike region and the past light cone. Within the safe domain, apparent cosmological singularities can be resolved by duality transformations and we briefly provide a physical picture of how this occurs. The unsafe domains represent true singularities where all field theoretic description of the physics breaks down. They violate the holographic principle. We argue that this structure provides a natural arrow of time for cosmology. All of the Kasner solutions, of the compactified SUGRA theory interpolate between the past and future light cones of the moduli space. We describe tentative generalizations of this analysis to moduli spaces with less SUSY.

Recently it has been proposed that a strange logarithmic expression for the so-called Barbero-Immirzi parameter, which is one of the ingredients that are necessary for loop quantum gravity (LQG) to predict the correct black hole entropy, is not a sign of an inconsistency of this approach to quantization of general relativity, but is a meaningful number that can be independently justified in classical GR. The alternative justification involves the knowledge of the real part of the frequencies of black hole quasinormal modes whose imaginary part blows up. In this paper we present an analytical derivation of the states with frequencies approaching a large imaginary number plus ln 3/8πG N M ; this constant has been only known numerically so far. We discuss the structure of the quasinormal modes for perturbations of various spin. Possible implications of these states for thermal physics of black holes and quantum gravity are mentioned and interpreted in a new way. A general conjecture about the asymptotic states is stated. e-print archive: http://lanl.arXiv.org/abs/gr-qc/0212096

Witten has recently proposed a string theory in twistor space whose Dinstanton contributions are conjectured to compute N = 4 super-Yang-Mills scattering amplitudes. An alternative string theory in twistor space was then proposed whose open string tree amplitudes reproduce the D-instanton computations of maximal degree in Witten's model. In this paper, a cubic open string field theory action is constructed for this alternative string in twistor space, and is shown to be invariant under parity transformations which exchange MHV and googly amplitudes. Since the string field theory action is gauge-invariant and reproduces the correct cubic super-Yang-Mills interactions, it provides strong support for the conjecture that the string theory correctly computes N -point super-Yang-Mills tree amplitudes.

There is evidence that one can compute tree-level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We give a partial explanation of the equivalence between the two computations, by showing that they could both be reduced to the same integral over a moduli space of singular curves, subject to some assumptions about the choices of integration contours. We also formulate a class of new "intermediate" prescriptions to calculate the same amplitudes.e-print archive: http://lanl.arXiv.org/abs/hep-th/0404085 SERGEI GUKOV, LUBOŠ MOTL, AND ANDREW NEITZKE Contents