Fractions Of Supersymmetry Research Articles

Supersymmetric AdS Solitons, Ground States, and Phase Transitions in Maximal Gauged Supergravity

We review some recent soliton solutions in a class of four-dimensional supergravity theories. The latter can be obtained from black hole solutions by means of a double Wick rotation. For special values of the parameters, the new configurations can be embedded in the gauged maximal N=8 theory and uplifted in the higher-dimensional D=11 theory. We also consider BPS soliton solutions, preserving a certain fraction of supersymmetry.

Partial breaking of arbitrary amount of d=3 supersymmetry

Among the solutions of string theory and supergravity which preserve some fraction of supersymmetry, the best known are those that leave one half of the supersymmetry unbroken, and there is a large number of field theory models with this pattern of supersymmetry breaking. However, a lot of brane configurations exist which preserve only $1/4$, $1/8$ or more exotic fractions of supersymmetry, and field theory side of these systems remains largely unexplored. To find whether the formalism of nonlinear realizations is useful in construction of models of this type, we consider the systems of some $N_0$ scalar and vector $N=1$, $d=3$ Goldstone supermultiplets. We find that it is possible to construct an $SO(N_0)$ invariant theory of $N_0$ scalar multiplets with $N_0$ broken supersymmetries. For $N_0=3$ or $N_0\geq 5$ its action is not of Nambu-Goto type and its structure remains universal for arbitrary $N_0$. The cases of $N_0=1,2$ correspond to the membranes in $D=4$ and $D=5$, respectively, while for $N_0=4$ some arbitrariness in the action remains, and with proper choice of parameters, it is possible to obtain the action of the membrane in $D=7$ in the bosonic limit. It is also shown that the $SO(N_0)$ invariant action of $N_0$ vector multiplets with $1/N_0$ pattern of supersymmetry breaking does not exist for arbitrary $N_0$.

Systematics of consistent truncations from generalised geometry

We present a generalised geometry framework for systematically constructing consistent truncations of ten- and eleven-dimensional supergravity preserving varying fractions of supersymmetry. Truncations arise when there is a reduced structure group GS of the exceptional generalised geometry, such that the intrinsic torsion is a GS -singlet. The matter content of the truncated theory follows from group-theoretical arguments, while the gauging is determined by the sub-algebra of generalised diffeomorphisms generated by the GS -singlet vectors. After discussing the general ideas across different spacetime dimensions and amounts of supersymmetry, we provide detailed formulae for truncations to gauged half-maximal supergravity in five dimensions. In particular, we establish an expression for the generalised metric on the exceptional tangent bundle, which determines the scalar truncation ansatz. As applications, we show that this formalism gives a simple derivation of a new consistent truncation of type IIB supergravity on β-deformed Lunin-Maldacena geometries, yielding half-maximal supergravity coupled to two vector multiplets, and of the truncation of eleven-dimensional supergravity on Maldacena-Núñez geometries, given by S4 twisted over a Riemann surface, which leads to half-maximal supergravity coupled to three vector multiplets.

CCNV Space-Times as Potential Supergravity Solutions

It is of interest to study supergravity solutions preserving a nonminimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the space-time admits a Killing spinor and hence a null or time-like Killing vector field. Any space-time admitting a covariantly constant null vector (CCNV) field belongs to the Kundt class of metrics and more importantly admits a null Killing vector field. We investigate the existence of additional non-space-like isometries in the class of higher-dimensional CCNV Kundt metrics in order to produce potential solutions that preserve some supersymmetries.

Supergravity backgrounds and symmetry superalgebras

We consider the bosonic sectors of supergravity theories in ten and eleven dimensions which correspond to the low energy limits of string theories and M-theory. The solutions of supergravity field equations are known as supergravity backgrounds and the number of preserved supersymmetries in those backgrounds are determined by Killing spinors. We provide some examples of supergravity backgrounds which preserve different fractions of supersymmetry. An important invariant for the characterization of supergravity backgrounds is their Killing superalgebras which are constructed out of Killing vectors and Killing spinors of the background. After constructing Killing superalgebras of some special supergravity backgrounds, we discuss about the possibilities of the extensions of these superalgebras to include the higher degree hidden symmetries of the background.

Heterotic supersymmetric backgrounds with compact holonomy revisited

We simplify the classification of supersymmetric solutions with compact holonomy of the Killing spinor equations of heterotic supergravity using the field equations and the additional assumption that the 3-form flux is closed. We determine all the fractions of supersymmetry that the solutions preserve and find that there is a restriction on the number of supersymmetries which depends on the isometry group of the background. We examine the geometry of spacetime in all cases. We find that the supersymmetric solutions of heterotic supergravity are associated with a large number of geometric structures which include seven-dimensional manifolds with G2 structure, six-dimensional complex and almost complex manifolds, and four-dimensional hyper-Kähler, Kähler and anti-self-dual Weyl manifolds.

Duality, entropy, and ADM mass in supergravity

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both "large" and "small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.

Supersymmetric Wilson loops at two loops

We study the quantum properties of certain BPS Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

Representations of superconformal algebras in the AdS7/4/CFT6/3 correspondence

We perform a general analysis of representations of the superconformal algebras OSp(8/4, ↛) and OSp(8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR’s by multiplication of the different types of massless conformal superfields (“supersingletons”). In particular, all “short multiplets” are classified. Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

REPRESENTATIONS OF SUPERCONFORMAL ALGEBRAS IN THE AdS7/4/CFT6/3 CORRESPONDENCE

We perform a general analysis of representations of the superconformal algebras OSp (8/4, ℝ) and OSp (8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

Superconformal interpretation of BPS states in AdS geometries

We carry out a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ∝), and OSp(8*/2N) and give their realization in superspace. We present a construction of their UIRs by multiplication of the different types of massless superfields (“supersingletons”). Particular attention is paid to the so-called “short multiplets.” Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

CONFORMAL SUPERFIELDS AND BPS STATES IN AdS4/7 GEOMETRIES

We carry out a general analysis of the representations of the superconformal algebras OSp(8/4, ℝ) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

Conformal primaries of OSp(8/4,Bbb R) and BPS states in AdS4

We derive short UIR's of the OSp(8/4,R) superalgebra of 3d N=8 superconformal field theories by the requirement that the highest weight states are annihilated by a subset of the super-Poincare odd generators. We then find a superfield realization of these BPS saturated UIR's as "composite operators" of the two basic ultrashort "supersingleton" multiplets. These representations are the AdS4 analogue of BPS states preserving different fractions of supersymmetry and are therefore suitable to classify perturbative and non-perturbative excitations of M-theory compactifications.

Central charges and Hamiltonians for 0-brane dynamics

We consider the general properties of central charges of 0-branes and associated duality invariants, in view of their double role, on the bulk and on the world volume (quantum mechanical) theory. A detailed study of the BPS condition for the mass spectrum arising from toroidal compactifications is given for 1/2, 1/4, and 1/8 BPS states in any dimension. As a by-product, we retrieve the U-duality invariant conditions on the charge (zero mode) spectrum and the orbit classification of BPS states preserving different fractions of supersymmetry. The BPS condition for 0-branes in theories with 16 supersymmetries in any dimension is also discussed.

BPS BLACK HOLES, SUPERSYMMETRY AND ORBITS OF EXCEPTIONAL GROUPS

We report on duality invariant constraints, which allow a classification of BPS black holes preserving different fractions of supersymmetry. We then relate this analysis to the orbits of the exceptional groups $E_{6(6)}, E_{7(7)}$, relevant for black holes in five and four dimensions.

Duality, central charges and entropy of extremal BPS black holes

We report on some general results on the physics of extremal BPS black holes in four and five dimensions. The duality-invariant entropy-formula for all N > 2 extended supergravities is derived. Its relation with the fixed-scalar condition for the black-hole “potential energy” wich extremizes the BPS mass is obtained. BPS black holes preserving different fractions of supersymmetry are classified in a U-duality invariant set up. The latter deals with different orbits of the fundamental representations of the exceptional groups E 7(7) and E 6(6). We comment upon the interpretation of these results in a string and M-theory framework.

BPS STATES AND SUPERSYMMETRY

We describe duality invariant constraints, which allow a classification of BPS states preserving different fractions of supersymmetry. We then relate this analysis to the orbits of the exceptional groups E6(6), E7(7), relevant for black holes in five and four dimensions. The orbits of O(P, Q) groups enter in the classification of BPS string in six dimensions.