12,651 research outputs found
Deformations of special geometry: in search of the topological string
The topological string captures certain superstring amplitudes which are also
encoded in the underlying string effective action. However, unlike the
topological string free energy, the effective action that comprises
higher-order derivative couplings is not defined in terms of duality covariant
variables. This puzzle is resolved in the context of real special geometry by
introducing the so-called Hesse potential, which is defined in terms of duality
covariant variables and is related by a Legendre transformation to the function
that encodes the effective action. It is demonstrated that the Hesse potential
contains a unique subsector that possesses all the characteristic properties of
a topological string free energy. Genus contributions are constructed
explicitly for a general class of effective actions associated with a
special-K\"ahler target space and are shown to satisfy the holomorphic anomaly
equation of perturbative type-II topological string theory. This identification
of a topological string free energy from an effective action is primarily based
on conceptual arguments and does not involve any of its more specific
properties. It is fully consistent with known results. A general theorem is
presented that captures some characteristic features of the equivalence, which
demonstrates at the same time that non-holomorphic deformations of special
geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement
Einstein-Cartan theory as a theory of defects in space-time
The Einstein-Cartan theory of gravitation and the classical theory of defects
in an elastic medium are presented and compared. The former is an extension of
general relativity and refers to four-dimensional space-time, while we
introduce the latter as a description of the equilibrium state of a
three-dimensional continuum. Despite these important differences, an analogy is
built on their common geometrical foundations, and it is shown that a
space-time with curvature and torsion can be considered as a state of a
four-dimensional continuum containing defects. This formal analogy is useful
for illustrating the geometrical concept of torsion by applying it to concrete
physical problems. Moreover, the presentation of these theories using a common
geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal
of Physics, revised version with typos correcte
Intrinsic Moment of Inertia of Membranes as bounds for the mass gap of Yang-Mills Theories
We obtain the precise condition on the potentials of Yang-Mills theories in
0+1 dimensions and D0 brane quantum mechanics ensuring the discretness of the
spectrum. It is given in terms of a moment of inertia of the membrane. From it
we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the
slow-mode regime. In particular we analyze the physical case D=3. The quantum
mechanical behavior of the theories, concerning its spectrum, is determined by
harmonic oscillators with frequencies given by the inertial tensor of the
membrane. We find a class of quantum mechanic potential polynomials of any
degree, with classical instabilities that at quantum level have purely discrete
spectrum.Comment: 12pages, Latex, minor changes, more explanatory comment
Comments on the global constraints in light-cone string and membrane theories
In the light-cone closed string and toroidal membrane theories, we associate
the global constraints with gauge symmetries. In the closed string case, we
show that the physical states defined by the BRS charge satisfy the
level-matching condition. In the toroidal membrane case, we show that the
Faddeev-Popov ghost and anti-ghost corresponding to the global constraints are
essentially free even if we adopt any gauge fixing condition for the local
constraint. We discuss the quantum double-dimensional reduction of the wrapped
supermembrane with the global constraints.Comment: 12 pages, typos corrected, to appear in JHE
The heat kernel of the compactified D=11 supermembrane with non-trivial winding
We study the quantization of the regularized hamiltonian, , of the
compactified D=11 supermembrane with non-trivial winding. By showing that
is a relatively small perturbation of the bosonic hamiltonian, we construct a
Dyson series for the heat kernel of and prove its convergence in the
topology of the von Neumann-Schatten classes so that is ensured to be
of finite trace. The results provided have a natural interpretation in terms of
the quantum mechanical model associated to regularizations of compactified
supermembranes. In this direction, we discuss the validity of the Feynman path
integral description of the heat kernel for D=11 supermembranes and obtain a
matrix Feynman-Kac formula.Comment: 19 pages. AMS LaTeX. A whole new section was added and some other
minor changes in style where mad
Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding
We analyze the Hamiltonian of the compactified D=11 supermembrane with
non-trivial central charge in terms of the matrix model constructed recently by
some of the authors. Our main result provides a rigorous proof that the quantum
Hamiltonian of the supersymmetric model has compact resolvent and thus its
spectrum consists of a discrete set of eigenvalues with finite multiplicity.Comment: 16 pages, final versio
Superfield Noether Procedure
We develop a superspace Noether procedure for supersymmetric field theories
in 4-dimensions for which an off-shell formulation in ordinary superspace
exists. In this way we obtain an elegant and compact derivation of the various
supercurrents in these theories. We then apply this formalism to compute the
central charges for a variety of effective actions. As a by-product we also
obtain a simple derivation of the anomalous superconformal Ward-identity in N=2
Yang-Mills theory. The connection with linearized supergravity is also
discussed.Comment: 47 pages, Latex, improved pedagogical presentation and references
adde
On BPS bounds in D=4 N=2 gauged supergravity II: general matter couplings and black hole masses
We continue the analysis of BPS bounds started in arXiv:1110.2688, extending
it to the full class of N=2 gauged supergravity theories with arbitrary vector
and hypermultiplets. We derive the general form of the asymptotic charges for
asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter
(mAdS_4) spacetimes. Some particular examples from black hole physics are given
to explicitly demonstrate how AdS and mAdS masses differ when solutions with
non-trivial scalar profiles are considered.Comment: 21 pages; v2 added reference, published version; v3 minor correction
N=2 Supergravity Lagrangian Coupled to Tensor Multiplets with Electric and Magnetic Fluxes
We derive the full N=2 supergravity Lagrangian which contains a symplectic
invariant scalar potential in terms of electric and magnetic charges. As shown
in reference [1], the appearance of magnetic charges is allowed only if tensor
multiplets are present and a suitable Fayet-Iliopoulos term is included in the
fermion transformation laws. We generalize the procedure in the quoted
reference by adding further a Fayet-Iliopoulos term which allows the
introduction of electric charges in such a way that the potential and the
equations of motion of the theory are symplectic invariant. The theory is
further generalized to include an ordinary electric gauging and the form of the
resulting scalar potential is given.Comment: 1+34 pages LaTeX, correction of a typo in the ungauged scalar
potentia
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