G. Sierra

Gauging the d = 5 Maxwell-Einstein Supergravity Theories: More on Jordan Algebras

Abstract We discuss in detail the possible gaugings, abelian and non-abelian, of a class of d = 5 Maxwell/Einstein supergravity theories for which the manifold of scalar fields is a symmetric coset space. We show that a U(1) “gauged” d =5 supergravity theory is possible with a vanishing scalar field potential, and we give necessary and sufficient conditions for this to occur. We discuss the d = 5 Yang-Mills/Einstein supergravity theories for both compact and non-compact gauge groups. We show that the “irreducibililty” of the “magical” subclass of d = 5 Maxwell/Einstein supergravity theories is preserved if and only if the Yang-Mills gauge group is SU(3,1). We expect that the irreducibility property of the “exceptional” d = 4 Maxwell/Einstein supergravity theory can similarly be preserved by gauging an SO∗(8) subgroup of its symmetry group E7(−25). Throughout we make extensive use of the underlying Jordan algebraic structure of N = 2 supergravity which we have established in previous work.

Two-dimensional supersymmetric nonlinear σ-models with torsion

Abstract We present a new kind of supersymmetric nonlinear σ-models in two dimensions characterized by the fact that the manifold of the scalar fields has torsion. In this way we obtain new geometries compatible with supersymmetry. If N 2 the manifolds are hermitian rather than kahlerian.

The unitary supermultiplets of d = 3 anti-de Sitter and d = 2 conformal superalgebras☆

We classify the d = 3 anti-de Sitter and d = 2 conformal superalgebras and give a general construction of their positive energy unitary representations. The corresponding supergroups are in general direct products G1 × G2 of two simple supergroups G1 and G2. We study in detail the cases when G1 (and/or G2) is SU(1,1/N) or Osp(2M/2, R).

Vanishing potentials in gauged N=2 supergravity: An application of Jordan algebras

Abstract We construct a class of N =2 supergravity theories in five spacetime dimensions with a gauged U(1) (i.e. minimal coupling to the gravitini) but vanishing scalar field potential. Supersymmetry is spontaneously broken. The models of this class are classified by their association with irreducible indempotents of a Jordan algebra. Similar results for N =2 supergravity in d =4 follow by dimensional reduction.

An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings

It is shown that there exists a correspondence between the theories of Jordan algebras and Freudenthal triple systems with classical particles and classical bosonic strings, respectively. In the latter case one is forced to consider the string embedded in a (D+2)-dimensional spacetime with two times and D spaces. The usual string is recovered upon imposing additional constraints on the (D+2) Virasoro algebra.

Analytic formulations of the density matrix renormalization group

We present two new analytic formulations of the density matrix renormalization group (DMRG) method. In these formulations we combine the block renormalization group (BRG) procedure with the variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising model in a transverse field (ITF model) and compute several of its critical properties, which are then compared with the old BRG results.

Singletons and superstrings

Abstract It is shown that the type IIA, IIB and heterotic superstring actions can be interpreted as the (8c, 8s), (8c, 8c) and (8c, 0) superconformally invariant two-dimensional singleton field theories of the three-dimensional anti-de Sitter supergroups OSp( 8 2 , R)c⊗OSp( 8 2 , R)s, OSp( 8 2 , R)c and OSp( 8 2 , R)c⊗Sp(2, R), respectively.

N = 2 Maxwell-matter-Einstein supergravities in d = 5,4 aand 3

Abstract We consider the coupling of the N = 2 Maxwell and matter multiplets to N = 2 supergravity in d = 5. It is shown that the scalar manifold factorizes into a quaternionic manifold for the matter scalar and a cubic hypersurfrace for the Maxwell scalar fields. This factorization is carried out to d = 4 and 3 through ordinary dimensional reduction. We study also the N = 2 theories obtained from the truncation of the N = 8 and N = 4 theories in those dimensions. In d = 3 we find a remarkable N = 4 theory described by the coset space ( E 8 (-24)/( E 7 × SU (2)))×( E 8 (-24)×/( E 7 × SU (2))) which would yield a Kac-Moody algebra of the type ( E 8 (1) × E 8 1 when dimensionally reduced to d = 2.

Quantum mechanical amplitude for string propagation

Abstract The quantum mechanical transition amplitude is calculated between an initial and a final string by using the canonical method based entirely on operators. The final expression for this amplitude is given in terms of the Jacobi ϑ4-function and admits a suggestive geometrical interpretation.

Causality on the world-sheet of the string

The (anti) commutator of the string coordinates xμ(ω,θ) and SAa(ω,θ) is studied for the open and closed free strings. By observing that this commutator is constant on each face of a polygonal pattern of the strings world-sheet, a close connection between causality and topology is arrived at.