Gödel space from wrapped M2-branes

Strings, branes, and gravity: TASI 99: Boulder, …, 2001

In the light of the duality between physics in the bulk of anti-de Sitter space and a conformal field theory on the boundary, we review the M 2, D3 and M 5 branes and how their near-horizon geometry yields the compactification of D = 11 supergravity on S 7 , Type IIB supergravity on S 5 and D = 11 supergravity on S 4 , respectively. We discuss the "Membrane at the End of the Universe" idea and its relation to the corresponding superconformal singleton theories that live on the boundary of the AdS 4 , AdS 5 and AdS 7 vacua. The massless sectors of these compactifications are described by the maximally supersymmetric D = 4, D = 5 and D = 7 gauged supergravities. We construct the non-linear Kaluza-Klein ansätze describing the embeddings of the U (1) 4 , U (1) 3 and U (1) 2 truncations of these supergravities, which admit 4-charge AdS 4 , 3-charge AdS 5 and 2charge AdS 7 black hole solutions. These enable us to embed the black hole solutions back in ten and eleven dimensions and reinterpret them as M 2, D3 and M 5 branes spinning in the transverse dimensions with the black hole charges given by the angular momenta of the branes. A comprehensive Appendix lists the field equations, symmetries and transformation rules of D = 11 supergravity, Type IIB supergravity, and the M 2, D3 and M 5 branes.

Journal of High Energy …, 2009

In this paper, we study the implementation of brane worlds in type II string theory. Starting with the NS/NS sector of type II string, we first compactify the (D+d++d−)-dimensional spacetime, and reduce the corresponding action to a D-dimensional effective action, where the topologies of Md+ and Md− are arbitrary. We further compactify one of the (D−1) spatial dimensions on an S1/Z2 orbifold, and derive the gravitational and matter field equations both in the bulk and on the branes. Then, we investigate two key issues in such a setup: (i) the radion stability and radion mass; and (ii) the localization of gravity, and the corresponding Kaluza-Klein (KK) modes. We show explicitly that the radion is stable and its mass can be in the order of GeV. In addition, the gravity is localized on the visible brane, and its spectrum of the gravitational KK towers is discrete and can have a mass gap of TeV, too. The high order Yukawa corrections to the 4-dimensional Newtonian potential is exponentially suppressed, and can be negligible. Applying such a setup to cosmology, we obtain explicitly the field equations in the bulk and the generalized Friedmann equations on the branes.

Nuclear Physics B, 1998

We investigate the effective worldvolume theories of branes in a background given by (the bosonic sector of) 10-dimensional massive IIA supergravity ("massive branes") and their M-theoretic origin. In the case of the solitonic 5-brane of type IIA superstring theory the construction of the Wess-Zumino term in the worldvolume action requires a dualization of the massive Neveu-Schwarz/Neveu-Schwarz target space 2-form field. We find that, in general, the effective worldvolume theory of massive branes contains new worldvolume fields that are absent in the massless case, i.e. when the mass parameter m of massive IIA supergravity is set to zero. We show how these new worldvolume fields can be introduced in a systematic way. In particular, we find new couplings between the massive solitonic 5-brane and the target space background, involving an additional worldvolume 1-form and 6-form. These new couplings have implications for the anomalous creation of branes. In particular, when a massive solitonic 5-brane passes through a D8-brane a stretched D6-brane is created. Similarly, in M-theory we find that when an M5-brane passes through an M9-brane a stretched Kaluza-Klein monopole is created. We show that pairs of massive branes of type IIA string theory can be viewed as the direct and double dimensional reduction of a single "massive M-brane" whose worldvolume theory is described by a gauged sigma model. For D-branes, the worldvolume gauge vector field becomes the Born-Infeld field of the 10-dimensional brane. The construction of the gauged sigma model requires that the 11dimensional background has a Killing isometry. This background can be viewed as an 11-dimensional rewriting of the 10-dimensional massive IIA supergravity theory. We present the explicit form and discuss the interpretation of (the bosonic sector of) this so-called "massive 11-dimensional supergravity theory". 8 Hats on spacetime fields and indices indicate they are 11-dimensional. Absence of hats indicates they are 10-dimensional. 9 We will heavily rely on this property. In combination with the identity

Journal of High Energy Physics, 2006

We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kähler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate for warped conical spaces that the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. Our approach automatically provides a solution to the problem of defining a holomorphic gauge coupling on wrapped D7-branes in a background with D3-branes. Finally, our results have applications to cosmological inflation models in which the inflaton is modeled by a D3-brane moving in a warped throat.

Journal of High Energy Physics, 2001

We study extremal and non-extremal generalizations of the regular non-abelian monopole solution of [23], interpreted in [9] as 5-branes wrapped on a shrinking S 2. Naively, the low energy dynamics is pure N = 1 supersymmetric Yang-Mills. However, our results suggest that the scale of confinement and chiral symmetry breaking in the Yang-Mills theory actually coincides with the Hagedorn temperature of the little string theory. We find solutions with regular horizons and arbitrarily high Hawking temperature. Chiral symmetry is restored at high energy density, corresponding to large black holes. But the entropy of the black hole solutions decreases as one proceeds to higher temperatures, indicating that there is a thermodynamic instability and that the canonical ensemble is ill-defined. For certain limits of the black hole solutions, we exhibit explicit non-linear sigma models involving a linear dilaton. In other limits we find extremal non-BPS solutions which may have some relevance to string cosmology.

Physics Letters B, 2000

We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy-momentum tensor is different from zero, the extra space-like dimension can be compactified with a single brane and show that the stability of the radius of compactification implies standard cosmology and vice versa. For a brane of finite thickness, we provide a solution such that the 4D Planck scale is related to the fundamental scale by the thickness of the brane. In this case, compactification of the extra dimension is unnecessary.

Physical Review D, 1997

In this paper we discuss the M -brane description for a N = 2 black hole. This solution is a result of the compactification of M -5-brane configurations over a Calabi-Yau threefold with arbitrary intersection numbers C ABC . In analogy to the D-brane description where one counts open string states we count here open M -2-branes which end on the M -5-brane.

2009

This is the written version of a talk given on 1 July 2009 at the XXV Max Born Symposium: the Planck Scale, held in Wrocaw, Poland. I review the possible transverse geometries to supersymmetric M2-brane config- urations and discuss the representation-theoretic description of their conjec- tured dual superconformal Chern-Simons theories.

Journal of High Energy Physics, 2000

We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality ; 2) Standard Model group ; 3) N = 1 or N = 0 supersymmetry ; 4) Three quark-lepton generations. We start such a program by studying configurations of D = 10, Type IIB D3-branes located at singularities. We study in detail the case of Z Z N N = 1, 0 orbifold singularities leading to the SM group or some left-right symmetric extension. In general, tadpole cancellation conditions require the presence of additional branes, e.g. D7-branes. For the N = 1 supersymmetric case the unique twist leading to three quark-lepton generations is Z Z 3 , predicting sin 2 θ W = 3/14 = 0.21. The models obtained are the simplest semirealistic string models ever built. In the non-supersymmetric case there is a three-generation model for each Z Z N , N > 4, but the Weinberg angle is in general too small. One can obtain a large class of D = 4 compact models by considering the above structure embedded into a Calabi Yau compactification. We explicitly construct examples of such compact models using Z Z 3 toroidal orbifolds and orientifolds, and discuss their properties. In these examples, global cancellation of RR charge may be achieved by adding anti-branes stuck at the fixed points, leading to models with hidden sector gravity-induced supersymmetry breaking. More general frameworks, like F-theory compactifications, allow completely N = 1 supersymmetric embeddings of our local structures, as we show in an explicit example. .

We consider an extension of the Randall-Sundrum model with three parallel 3-branes in a 5-dimensional spacetime. This new construction, apart from providing a solution to the Planck hierarchy problem, has the advantage that the SM fields are confined on a positive tension brane. The study of the phenomenology of this model reveals an anomalous first KK state which is generally much lighter than the remaining tower and also much more strongly coupled to matter. Bounds on the parameter space of the model can be placed by comparison of specific processes with the SM background as well as by the latest Cavendish experiments. The model suggests a further exotic possibility if one drops the requirement of solving the hierarchy problem. In this case gravity may result from the exchange of the ordinary graviton plus an ultralight KK state and modifications of gravity may occur at both small and extremely large scales.