Narrow Results

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle $({𝒮},D,\omega )$ defined over the scalar manifold ${ℳ}$. The construction uses a taming of $({𝒮},\omega )$, which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of ${ℳ}$ to the bundle ${𝒮}$ and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over ${ℳ}$ and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from ${𝒩}=2$ supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

A bosonic sector of the four-dimensional low-energy heterotic string theory with two Abelian gauge fields is considered in the stationary case. A new 4× 4 unitary null-curvature matrix representation of the theory is derived and the corresponding formulation based on the use of a new 2 × 2 Ernst type matrix complex potential is developed. The group of hidden symmetries is described and classified in the matrix-valued quasi general relativity form. A subgroup of charge symmetries is constructed and representation which transforms linearly under the action of this symmetry subgroup is established. Also the solution generation procedure based on the application of the total charge symmetry subgroup to the stationary Einstein–Maxwell theory is analyzed.

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann–Robertson–Walker (FRW) equations and Cardy–Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of five-dimensional dS background as it happens in the AdS/CFT correspondence.

We consider M-theory on AdS₄ × N^0,1,0 where N^0,1,0 = (SU(3) × (2))/(SU(2) × U(1)). We review a Penrose limit of AdS₄ × N^0,1,0 that provides the pp-wave geometry of AdS₄ × S⁷. There exists a subsector of three-dimensional dual gauge theory, by taking both the conformal dimension and R-charge large with the finiteness of their difference, which has enhanced maximal supersymmetry. We identify operators in the gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the gauge theory operators originating from both short vector multiplet and long gravitino multiplet fall into supermultiplets.

The explicit form of the fermionic zero-modes in the five-brane backgrounds of type IIA and IIB supergravity theories is investigated. In type IIA five-brane background there are four zero-modes of gravitinos and dilatinos. In type IIB five-brane background four zero-modes of dilatinos and no zero-modes of gravitinos are found. These zero-modes indicate the four-fermion condensates which have been suggested in a calculation of the tension of the D-brane in five-brane backgrounds.

The theory of inflation will be investigated as well as supersymmetry breaking in the context of supergravity, incorporating the target-space duality and the nonperturbative gaugino condensation in the hidden sector. We found an inflationary trajectory of a dilaton field and a condensate field which breaks supersymmetry at once. The model satisfies the slow-roll condition which solves the η-problem. When the particle rolls down along the minimized trajectory of the potential V(S,Y) at a duality invariant point of T=1, we can obtain the e-fold value ~57. And then the cosmological parameters obtained from our model well match the recent WMAP data combined with other experiments. This observation suggests one to consider the string-inspired supergravity as a fundamental theory of the evolution of the universe as well as the particle theory.

Using the right representation in the evaluation of the creation probability of the universe, one can show that the external dimension of the Freund–Rubin model is min(s,n-s), where s is the rank of the antisymmetric field strength in the model.

We consider a particular solution to Slavnov–Taylor identity in four-dimensional supergravity. The consideration is performed for pure supergravity, no matter superfields are included. The solution is obtained by inserting dressing functions into ghost part of the classical action for supergravity. As a consequence, physical part of the effective action is local invariant with respect to diffeomorphism and structure groups of transformation for dressed effective superfields of vielbein and spin connection.

We present a simple mechanism to eliminate cosmological constants both in supersymmetric and non-supersymmetric theories. This mechanism is based on the Hodge (Poincaré) duality between a 0-form and D-form field strengths in D-dimensional spacetime. The new key ingredient is the introduction of an extra Chern–Simons term into the D-form field strength H dual to the 0-form field strength. Our formulation can also be made consistent with supersymmetry. Typical applications to four-dimensional N = 1 supergravity and to ten-dimensional type IIA supergravity are given. The success of our formulation for both supersymmetric and non-supersymmetric systems strongly indicates the validity of our mechanism even after supersymmetry breakings at the classical level. Our mechanism may well be applicable to quantized systems, at least for supersymmetric cases with fundamental D-brane actions available.

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λ_a and Ramond Grassmannian vector in the spinor realization⁴² are proposed. The map of supergravity background into composite supercoordinates: valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector and to vanish for the θ components with the same chiralities. The deformations in the (super)twistor picture are discussed.

We have applied the method of dualization to construct the coset realization of the bosonic sector of the , D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction.

We investigate split supersymmetry (SUSY) within a supergravity framework, where local SUSY is broken by the F-term of a hidden sector chiral superfield X. With reasonably general assumptions, we show that the fermionic component of X will always have mass within a TeV. Though its coupling to the observable sector superfields is highly suppressed in TeV scale SUSY, we show that it can be enhanced by many orders in split SUSY, leading to its likely participation in accelerator phenomenology. We conclude with a specific example of such a scenario in a string based supergravity model.

We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in terms of a linear system for the fluxes and the geometry of spacetime. The solutions of this linear system express some of the fluxes in terms of the spacetime geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. We also present some of the recent applications like the classification of maximally supersymmetric G-backgrounds in IIB, this includes the most general pp-wave solution preserving 1/2 supersymmetry, and the classification of N = 31 backgrounds in ten and eleven dimensions.

Supersymmetry and extra dimensions are the two most promising candidates for new physics at the TeV scale. Supersymmetric particles or extra-dimensional effects could soon be observed at the Large Hadron Collider. We propose a simple but effective method to discriminate the two models: the analysis of isolated leptons with high transverse momentum. Black hole events are simulated with the CATFISH black hole generator. Supersymmetry simulations use a combination of PYTHIA and ISAJET, the latter providing the mass spectrum. Our results show that the measure of the dilepton invariant mass provides a promising signature to differentiate supersymmetry and black hole events at the Large Hadron Collider. Analysis of event-shape variables and multilepton events complement and strengthen this conclusion.

In this paper we discuss a method of generating solutions of the Einstein equations on supersymmetric and non-supersymmetric backgrounds. The method involves the embedding of a supersymmetric spacetime into another, curved spacetime. We present three examples with constituent spacetimes which support "charges", one of which was known previously and the other two of which are new. All of the examples have PP-waves as one of the embedding constituents.

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by P. Ramond, S.-S. Kim and myself where we describe the supergravity in the light-cone formalism. We show how the Cremmer–Julia E₇₍₇₎ nonlinear symmetry is implemented and how the full supermultiplet is a representation of the E₇₍₇₎ symmetry. I also show how the E₇₍₇₎ symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.

The complete supersymmetric classical Batalin–Vilkovisky action for 11-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.

No-scale supergravity is a framework where it is possible to naturally explain radiative electroweak symmetry breaking and correlate it with the effective SUSY breaking scale. Many string compactifications have a classical no-scale structure, resulting in a one-parameter model (OPM) for the supersymmetry breaking soft terms, which results in a highly constrained subset of mSUGRA. We investigate the allowed supersymmetry parameter space for a generic one-parameter model taking into account the most recent experimental constraints. We also survey the possible signatures which may be observable at the Large Hadron Collider (LHC). Finally, we compare collider signatures of OPM to those from a model with non-universal soft terms, in particular those of an intersecting D6-brane model.

We propose a supersymmetric extension of the dynamical dark energy function and the scalar (super)potential in supergravity. Our model is viable in the Einstein approximation, and also has an analytic (regular) scalar potential. The hidden sector responsible for spontaneous supersymmetry breaking is also given.

We comment on consistent truncation over higher-dimensional sphere in supergravity.