17,179 research outputs found
S-duality and the prepotential in N=2* theories (I): the ADE algebras
The prepotential of N=2* supersymmetric theories with unitary gauge groups in
an Omega-background satisfies a modular anomaly equation that can be
recursively solved order by order in an expansion for small mass. By requiring
that S-duality acts on the prepotential as a Fourier transform we generalise
this result to N=2* theories with gauge algebras of the D and E type and show
that their prepotentials can be written in terms of quasi-modular forms of
SL(2,Z). The results are checked against microscopic multi-instanton calculus
based on localization for the A and D series and reproduce the known
1-instanton prepotential of the pure N=2 theories for any gauge group of ADE
type. Our results can also be used to obtain the multi-instanton terms in the
exceptional theories for which the microscopic instanton calculus and the ADHM
construction are not available.Comment: 33 pages, LaTeX2e, added references, version to be published in JHE
A note on supersymmetric D-brane dynamics
We study the spin dependence of D-brane dynamics in the Green-Schwarz
formalism of boundary states. In particular we show how to interpret insertion
of supercharges on the boundary state as sources of non-universal spin effects
in D-brane potentials. In this way we find for a generic (D)p-brane, potentials
going like corresponding to interactions between the
different components of the D-brane supermultiplet. From the eleven dimensional
point of view, these potentials arise from the exchange of field strengths
corresponding to the graviton and the three form, coupled non-minimally to the
branes. We show how an annulus computation truncated to its massless
contribution is enough to reproduce these next-to-leading effects, meaning in
particular that the one-loop (M)atrix theory effective action should encode all
the spin dependence of low-energy supergravity interactions.Comment: LaTex file, 12 pages, no figures, some corrections in last section
and references added; version to appear in Physics Letters
Real sector of the nonminimally coupled scalar field to self-dual gravity
A scalar field nonminimally coupled to gravity is studied in the canonical
framework, using self-dual variables. The corresponding constraints are first
class and polynomial. To identify the real sector of the theory, reality
conditions are implemented as second class constraints, leading to three real
configurational degrees of freedom per space point. Nevertheless, this
realization makes non-polynomial some of the constraints. The original complex
symplectic structure reduces to the expected real one, by using the appropriate
Dirac brackets. For the sake of preserving the simplicity of the constraints,
an alternative method preventing the use of Dirac brackets, is discussed. It
consists of converting all second class constraints into first class by adding
extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure
Optimization of soliton ratchets in inhomogeneous sine-Gordon systems
Unidirectional motion of solitons can take place, although the applied force
has zero average in time, when the spatial symmetry is broken by introducing a
potential , which consists of periodically repeated cells with each cell
containing an asymmetric array of strongly localized inhomogeneities at
positions . A collective coordinate approach shows that the positions,
heights and widths of the inhomogeneities (in that order) are the crucial
parameters so as to obtain an optimal effective potential that yields
a maximal average soliton velocity. essentially exhibits two
features: double peaks consisting of a positive and a negative peak, and long
flat regions between the double peaks. Such a potential can be obtained by
choosing inhomogeneities with opposite signs (e.g., microresistors and
microshorts in the case of long Josephson junctions) that are positioned close
to each other, while the distance between each peak pair is rather large. These
results of the collective variables theory are confirmed by full simulations
for the inhomogeneous sine-Gordon system
Multi instanton tests of holography
Gauge theories living on stacks of D7-branes are holographically related to
IIB gravitational backgrounds with a varying axion-dilaton field (F-theory).
The axion-dilaton field is generated by D7, O7 and D-instanton sources and can
be written in terms of the chiral correlators of the eight dimensional gauge
theory living on the D7-branes. Using localization techniques, we prove that
the same correlators determine the gauge coupling of the four-dimensional N=2
supersymmetric SU(2) gauge theories living on the elementary D3-brane which
probes the F-theory geometries.Comment: 18 page
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