We discuss the full nonlinear Kaluza-Klein (KK) reduction of the original formulation of d=11 supergravity on AdS 7 × S 4 to gauged maximal (N=4) supergravity in 7 dimensions. We derive the full nonlinear embedding of the d = 7 fields in the d = 11 fields ("the ansatz") and check the consistency of the ansatz by deriving the d=7 supersymmetry laws from the d=11 transformation laws in the various sectors. The ansatz itself is nonpolynomial but the final d = 7 results are polynomial. The correct d = 7 scalar potential is obtained. For most of our results the explicit form of the matrix U connecting the d = 7 gravitino to the Killing spinor is not needed, but we derive the equation which U has to satisfy and present the general solution. Requiring that the expression δF = dδA in d = 11 can be written as δd(f ields in d = 7), we find the ansatz for the 4-form F . It satisfies the Bianchi identities. The corresponding ansatz for the 3-form A modifies the geometrical proposal by Freed et al. by including d = 7 scalar fields. A first order formulation for A in d = 11 is needed to obtain the d=7 supersymmetry laws and the action for the nonabelian selfdual antisymmetric tensor field S αβγ,A . Therefore selfduality in odd dimensions originates from a first order formalism in higher dimensions.

We show that there exists a consistent truncation of 11 dimensional supergravity to the 'massless' fields of maximal (N=4) 7 dimensional gauged supergravity. We find the complete expressions for the nonlinear embedding of the 7 dimensional fields into the 11 dimensional fields, and check them by reproducing the d=7 susy transformation laws from the d=11 laws in various sectors. In particular we determine explicitly the matrix U which connects the Killing spinors to the gravitinos in the KK ansatz, and the dependence of the 4-index field strength on the scalars. This is the first time a complete nonlinear KK reduction of the original d=11 supergravity on a nontrivial compact space has been explicitly given. We need a first order formulation for the 3 index tensor field A ΛΠΣ in d=11 to reproduce the 7 dimensional result. The concept of 'self-duality in odd dimensions' is thus shown to originate from first order formalism in higher dimensions. For the AdS-CFT correspondence, our results imply that one can use 7d gauged supergravity (without further massive modes) to compute certain correlators in the d=6 (0,2) CFT at leading order in N. This eliminates an ambiguity in the formulation of the correspondence.The question whether in general a consistent Kaluza-Klein (KK) truncation exists at the nonlinear level is an old problem. For tori, the consistency is easy to prove, but for more complicated compact spaces little is known. In supergravity (sugra), the truncation of d=11 sugra on AdS 4 × S 7 to maximal d = 4 gauged sugra was intensively studied 15 years ago [1], culminating in a series of papers by de Wit and Nicolai [2,3]. The interest in those days was to find realistic 4 dimensional models from spontaneous compactification of maximal 11 dimensional sugra. Recent developments in the AdS-CFT correspondence [4,5,6,7,8] have renewed interest in AdS compactifications

We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the local ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be characterized by a spatially varying "entanglement temperature." Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally, we give a CFT derivation of a set of constraint equations obeyed by the entanglement entropy of excited states in any dimension. Previously, these equations were derived in the context of holography.

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2-holonomy without fluxes. This gives stable vacua with softly broken susy, grand unification and a distinctive spectrum of TeV and sub-TeV sparticle masses. .Jv 14.80.Ly Stabilizing Hierarchies and ModuliM theory (and its weakly coupled string limits) is a consistent quantum theory including gravity, particle physics and much more. Although apparently unique, the theory has a large number of solutions, manifested by the presence of moduli: massless scalar fields with classically undetermined vacuum expectation values (vevs), whose values determine the masses and coupling constants of the low energy physics.In recent years, there has been substantial progress in understanding mechanisms which stabilize moduli in various corners of the M theory moduli space. In particular, the stabilization of all moduli by magnetic fields (fluxes) in the extra dimensions, perhaps also combined with other quantum effects, has been reasonably well understood in the context of Type IIB string theory [1,2], M theory [3] and Type IIA string theory [4]. After stabilizing the moduli, one still has to explain why M W /m pl ∼ 10 −16 . The effective potential of these compactifications fits into the framework of a low energy supergravity theory in four dimensions. A well known property of the latter is that there is a universal contribution to scalar masses of order the gravitino mass m 3/2 . Therefore, without miraculous cancellations, in theories in which m 3/2 is large, the Higgs mass is also large. In M theory and Type IIA flux vacua the vacuum superpotential is O(1) or larger in Planck units. This gives a large m 3/2 (unless the volume of the extra dimensions is large, ruining standard unification). In heterotic flux vacua [5] m 3/2 can be smaller, but only by a few orders of magnitude. Thus, in these vacua, stabilizing the moduli using fluxes fails to solve the hierarchy problem, viz. to generate and stabilize the hierarchy between the electroweak and Planck scales.In Type IIB theory, this is not so: m 3/2 can be tuned small by choosing fluxes. One can also address the possibility of generating the hierarchy through warping [6] in this framework [1]. The hierarchy problem is less well understood in other corners of the M theory moduli space.Our focus will be M theory, and we will henceforth switch off all the fluxes else the hierarchy will be destroyed. Supersymmetry then implies that the seven extra dimensions form a space X with G 2 -holonomy. In these vacua, non-Abelian gauge fields are localized along three dimensional submanifolds Q ⊂ X at which there is an orbifold singularity [7] and chiral fermions are localized at points at which there are conical singularities [8,9,10].These vacua can have interesting phenomenological features, independently of how moduli are stabilized: the Yukawa couplings are hierarchical; proton decay proceeds at dimension six with disti...

We discuss Regge trajectories of dynamical mesons in large-N c QCD, using the supergravity background describing N c D4-branes compactified on a thermal circle. The flavor degrees of freedom arise from the addition of N f N c D6 probe branes. Our work provides a string theoretical derivation, via the gauge/string correspondence, of a phenomenological model describing the meson as rotating point-like massive particles connected by a flux string. The massive endpoints induce nonlinearities for the Regge trajectory. For light quarks the Regge trajectories of mesons are essentially linear. For massive quarks our trajectories qualitatively capture the nonlinearity detected in lattice calculations.