1,257 research outputs found
Potentials for (p,0) and (1,1) supersymmetric sigma models with torsion
Using (1,0) superfield methods, we determine the general scalar potential
consistent with off-shell (p,0) supersymmetry and (1,1) supersymmetry in
two-dimensional non-linear sigma models with torsion. We also present an
extended superfield formulation of the (p,0) models and show how the (1,1)
models can be obtained from the (1,1)-superspace formulation of the gauged, but
massless, (1,1) sigma model.Comment: 11 page
TransverseDiff gravity is to scalar-tensor as unimodular gravity is to General Relativity
Transverse Diffeomorphism (TDiff) theories are well-motivated theories of
gravity from the quantum perspective, which are based upon a gauge symmetry
principle. The main contribution of this work is to firmly establish a
correspondence between TransverseDiff and the better-known scalar-tensor
gravity --- in its more general form ---, a relation which is completely
analogous to that between unimodular gravity and General Relativity. We then
comment on observational aspects of TDiff. In connection with this proof, we
derive a very general rule that determines under what conditions the procedure
of fixing a gauge symmetry can be equivalently applied before the variational
principle leading to the equations of motion, as opposed to the standard
procedure, which takes place afterwards; this rule applies to gauge-fixing
terms without derivatives.Comment: 10 pages; amsart style; v3: version as appeared in JCAP, redaction
improve
On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings
We provide a simple lagrangian interpretation of the meaning of the
semi-relative condition in closed string theory. Namely, we show how the
semi-relative condition is equivalent to the requirement that physical
operators be cohomology classes of the BRS operators acting on the space of
local fields {\it covariant} under world-sheet reparametrizations. States
trivial in the absolute BRS cohomology but not in the semi-relative one are
explicitly seen to correspond to BRS variations of operators which are not
globally defined world-sheet tensors. We derive the covariant expressions for
the observables of topological gravity. We use them to prove a formula that
equates the expectation value of the gravitational descendant of ghost number 4
to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199
Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
The gauged sigma-model argument that string backgrounds related by T-dual
give equivalent quantum theories is revisited, taking careful account of global
considerations. The topological obstructions to gauging sigma-models give rise
to obstructions to T-duality, but these are milder than those for gauging: it
is possible to T-dualise a large class of sigma-models that cannot be gauged.
For backgrounds that are torus fibrations, it is expected that T-duality can be
applied fibrewise in the general case in which there are no globally-defined
Killing vector fields, so that there is no isometry symmetry that can be
gauged; the derivation of T-duality is extended to this case. The T-duality
transformations are presented in terms of globally-defined quantities. The
generalisation to non-geometric string backgrounds is discussed, the conditions
for the T-dual background to be geometric found and the topology of T-folds
analysed.Comment: Minor corrections and addition
A Two-loop Test of Buscher's T-duality I
We study the two loop quantum equivalence of sigma models related by
Buscher's T-duality transformation. The computation of the two loop
perturbative free energy density is performed in the case of a certain
deformation of the SU(2) principal sigma model, and its T-dual, using
dimensional regularization and the geometric sigma model perturbation theory.
We obtain agreement between the free energy density expressions of the two
models.Comment: 28 pp, Latex, references adde
Fermi surface renormalization in Hubbard ladders
We derive the one-loop renormalization equations for the shift in the
Fermi-wavevectors for one-dimensional interacting models with four Fermi-points
(two left and two right movers) and two Fermi velocities v_1 and v_2. We find
the shift to be proportional to (v_1-v_2)U^2, where U is the Hubbard-U. Our
results apply to the Hubbard ladder and to the t_1-t_2 Hubbard model. The
Fermi-sea with fewer particles tends to empty. The stability of a saddle point
due to shifts of the Fermi-energy and the shift of the Fermi-wavevector at the
Mott-Hubbard transition are discussed.Comment: 5 pages, 4 Postscript figure
Holonomy groups and W-symmetries
Irreducible sigma models, i.e. those for which the partition function does
not factorise, are defined on Riemannian spaces with irreducible holonomy
groups. These special geometries are characterised by the existence of
covariantly constant forms which in turn give rise to symmetries of the
supersymmetric sigma model actions. The Poisson bracket algebra of the
corresponding currents is a W-algebra. Extended supersymmetries arise as
special cases.Comment: pages 2
Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities
In this paper a two dimensional non-linear sigma model with a general
symplectic manifold with isometry as target space is used to study symplectic
blowing up of a point singularity on the zero level set of the moment map
associated with a quasi-free Hamiltonian action. We discuss in general the
relation between symplectic reduction and gauging of the symplectic isometries
of the sigma model action. In the case of singular reduction, gauging has the
same effect as blowing up the singular point by a small amount. Using the
exponential mapping of the underlying metric, we are able to construct
symplectic diffeomorphisms needed to glue the blow-up to the global reduced
space which is regular, thus providing a transition from one symplectic sigma
model to another one free of singularities.Comment: 32 pages, LaTex, THEP 93/24 (corrected and expanded(about 5 pages)
version
From E_8 to F via T
We argue that T-duality and F-theory appear automatically in the E_8 gauge
bundle perspective of M-theory. The 11-dimensional supergravity four-form
determines an E_8 bundle. If we compactify on a two-torus, this data specifies
an LLE_8 bundle where LG is a centrally-extended loopgroup of G. If one of the
circles of the torus is smaller than sqrt(alpha') then it is also smaller than
a nontrivial circle S in the LLE_8 fiber and so a dimensional reduction on the
total space of the bundle is not valid. We conjecture that S is the circle on
which the T-dual type IIB theory is compactified, with the aforementioned torus
playing the role of the F-theory torus. As tests we reproduce the T-dualities
between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find
the desired F-theory monodromy. Using Hull's proposal for massive IIA, this
realization of T-duality allows us to confirm that the Romans mass is the
central extension of our LE_8. In addition this construction immediately
reproduces the conjectured formula for global topology change from T-duality
with H-flux.Comment: 25 pages, 4 eps figure
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