arXiv subjects

Lubos Motl

Publications and source records attributed to Lubos Motl.

At least 19 recordsLinked to original sources

arXiv2007

Higher-order corrections to mass-charge relation of extremal black holes

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 so-called 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.

hep-th↗

arXiv2006

The String Landscape, Black Holes and Gravity as the Weakest Force

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 Lambda=g M_{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 Lambda. 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.

hep-th↗

arXiv2004

Equivalence of twistor prescriptions for super Yang-Mills

There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are chosen in a specific way, by showing that they can both be reduced to the same integral over a moduli space of singular curves. We also formulate a class of new ``intermediate'' prescriptions to calculate the same amplitudes.

hep-th↗

arXiv2004

Cubic Twistorial String Field Theory

Witten has recently proposed a string theory in twistor space whose D-instanton 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.

hep-th↗

arXiv2003

An analytical computation of asymptotic Schwarzschild quasinormal frequencies

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 another sign of the inconsistency of this approach to quantization of General Relativity, but is rather 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 states 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 / 8 pi M; this constant has been only known numerically so far. We discuss the structure of the quasinormal states 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. Although our main result lends some credibility to LQG, we also review some of its claims in a critical fashion and speculate about its possible future relevance for Quantum Gravity.

gr-qc↗

arXiv2003

Asymptotic black hole quasinormal frequencies

We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d>=4 and Reissner-Nordstrom black holes in d=4, in the limit of infinite damping. For Schwarzschild in d>=4 we find that the asymptotic real part is T_Hawking.log(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d=4. For Reissner-Nordstrom in d=4 we find a specific generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for electromagnetic-gravitational perturbations. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane; the analysis depends essentially on the behavior of the potential in the "unphysical" region near the black hole singularity.

hep-th↗

arXiv2003

Matrix string theory, contact terms, and superstring field theory

In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N limit in matrix string theory, in particular in relation with conformal perturbation theory around the orbifold SCFT that reproduces light-cone string perturbation theory. We show how the scaling with N is directly related to measures on the moduli space of Riemann surfaces. The scaling dimension 3 of the Mandelstam vertex as reproduced by the twist field interaction is in this way related to the dimension 3(h-1) of the moduli space. We analyze the structure and scaling of the higher order twist fields that represent the contact terms. We find one relevant twist field at each order. More generally, the structure of string field theory seems more transparent in the twist field formalism. Finally we also investigate the modifications necessary to describe the pp-wave backgrounds in the light-cone gauge and we interpret a diagram from the BMN limit as a stringy diagram involving the contact term.

hep-th↗

arXiv2003

Heterotic plane wave matrix models and giant gluons

In this paper we define and study a matrix model describing the M-theory plane wave background with a single Horava-Witten domain wall. In the limit of infinite mu, the matrix model action becomes quadratic and we can identify the matrix Hamiltonian with a regularized Hamiltonian for hemispherical membranes that carry fermionic degrees of freedom on their boundaries. The number of fermionic degrees of freedom must be sixteen; this condition arises naturally in the framework of the matrix model. We can also prove the exact E_8 symmetry of the spectrum around the membrane vacua at infinite mu, which arises as a current algebra at level one just as in the heterotic string. We also find the full E_8 gauge multiplet as well as the multiple-gluon states, carried by collections of hemispherical membranes. Finally we discuss the dual description of the hemispherical membranes in terms of spherical fivebranes immersed in the domain wall; we identify the correct vacuum of the matrix model and make some preliminary comparisons with the (1,0) superconformal field theory.

hep-th↗

arXiv2002

Deconstructing (2,0) and Little String Theories

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.

hep-th↗

arXiv2002

PP-Wave / CFT_2 Duality

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.

hep-th↗

arXiv2002

PP-wave string interactions from perturbative Yang-Mills 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 lambda'=g_{YM}^2 N/J^2=1/(mu p^+ alpha')^2. We study Yang-Mills theory at small lambda' (large mu) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g_2^2=J^4/N^2=(4 pi g_s)^2 (mu p^+ alpha')^4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g_2 sqrt{lambda'} 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 lambda' 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 earlier computation.

hep-th↗

arXiv2001

Nonperturbative Formulations of Superstring Theory

After a short introduction to Matrix theory, we explain how can one generalize matrix models to describe toroidal compactifications of M-theory and the heterotic vacua with 16 supercharges. This allows us, for the first time in history, to derive the conventional perturbative type IIA string theory known in the 80s within a complete and consistent nonperturbative framework, using the language of orbifold conformal field theory and conformal perturbation methods. A separate chapter is dedicated to the vacua with Horava-Witten domain walls that carry E8 gauge supermultiplets. Those reduce the gauge symmetry of the matrix model from U(N) to O(N). We also explain why these models contain open membranes. The compactification of M-theory on T4 involves the so-called (2,0) superconformal field theory in six dimensions, compactified on T5. A separate chapter describes an interesting topological contribution to the low energy equations of motion on the Coulomb branch of the (2,0) theory that admits a skyrmionic solution that we call ``knitting fivebranes''. Then we return to the orbifolds of Matrix theory and construct a formal classical matrix model of the Scherk-Schwarz compactification of M-theory and type IIA string theory as well as type 0 theories. We show some disastrous consequences of the broken supersymmetry. Last two chapters describe a hyperbolic structure of the moduli spaces of one-dimensional M-theory.

hep-th↗

arXiv2001

Melvin Matrix Models

In this short note we construct the DLCQ description of the flux seven-branes in type IIA string theory and discuss its basic properties. The matrix model involves dipole fields. We explain the relation of this nonlocal matrix model to various orbifolds. We also give a spacetime interpretation of the Seiberg-Witten-like map, proposed in a different context first by Bergman and Ganor, that converts this matrix model to a local, highly nonlinear theory.

hep-th↗

arXiv2000

On Anthropic Solutions of the Cosmological Constant Problem

Motivated by recent work of Bousso and Polchinski (BP), we study theories which explain the small value of the cosmological constant using the anthropic principle. We argue that simultaneous solution of the gauge hierarchy problem is a strong constraint on any such theory. We exhibit three classes of models which satisfy these constraints. The first is a version of the BP model with precisely two large dimensions. The second involves 6-branes and antibranes wrapped on supersymmetric 3-cycles of Calabi-Yau manifolds, and the third is a version of the irrational axion model. All of them have possible problems in explaining the size of microwave background fluctuations. We also find that most models of this type predict that all constants in the low energy Lagrangian, as well as the gauge groups and representation content, are chosen from an ensemble and cannot be uniquely determined from the fundamental theory. In our opinion, this significantly reduces the appeal of this kind of solution of the cosmological constant problem. On the other hand, we argue that the vacuum selection problem of string theory might plausibly have an anthropic, cosmological solution.

hep-th↗

arXiv1999

A nonsupersymmetric matrix orbifold

We construct the matrix description for a twisted version of the IIA string theory on S^1 with fermions antiperiodic around a spatial circle. The result is a 2+1-dimensional U(N) x U(N) nonsupersymmetric Yang-Mills theory with fermionic matter transforming in the (N,Nbar). The two U(N)'s are exchanged if one goes around a twisted circle of the worldvolume. Relations with Type 0 theories are explored and we find Type 0 matrix string limits of our gauge theory. We argue however that most of these results are falsified by the absence of SUSY nonrenormalization theorems and that the models do not in fact have a sensible Lorentz invariant space time interpretation.

hep-th↗

arXiv1999

On the Hyperbolic Structure of Moduli Spaces With 16 SUSYs

We study the asymptotic limits of the heterotic string theories compactified on tori. We find a bilinear form uniquely determined by dualities which becomes Lorentzian in the case of one spacetime dimension. For the case of the SO(32) theory, the limiting descriptions include SO(32) heterotic strings, type I, type IA and other T-duals, M-theory on K3, type IIA theory on K3 and type IIB theory on K3 and possibly new limits not understood yet.

hep-th↗

arXiv1998

Dualities versus Singularities

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.

hep-th↗

arXiv1998

Equations of the (2,0) Theory and Knitted Fivebranes

We study non-linear corrections to the low-energy description of the (2,0) theory. We argue for the existence of a topological correction term similar to the C3 wedge X8(R) in M-theory. This term can be traced to a classical effect in supergravity and to a one-loop diagram of the effective 4+1D Super Yang-Mills. We study other terms which are related to it by supersymmetry and discuss the requirements on the subleading correction terms from M(atrix)-theory. We also speculate on a possible fundamental formulation of the theory.

hep-th↗