371 research outputs found
Multi-Matrix Models: Integrability Properties and Topological Content
We analyze multi--matrix chain models. They can be considered as
multi--component Toda lattice hierarchies subject to suitable coupling
conditions. The extension of such models to include extra discrete states
requires a weak form of integrability. The discrete states of the --matrix
model are organized in representations of . We solve exactly the
Gaussian--type models, of which we compute several all-genus correlators. Among
the latter models one can classify also the discretized string theory,
which we revisit using Toda lattice hierarchy methods. Finally we analyze the
topological field theory content of the --matrix models: we define primary
fields (which are ), metrics and structure constants and prove that
they satisfy the axioms of topological field theories. We outline a possible
method to extract interesting topological field theories with a finite number
of primaries.Comment: 31 pages, Late
Matrix String Theory, 2D SYM Instantons and affine Toda systems
Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we
show that in the U(N) SYM Matrix theory there exist classical BPS instantons
which interpolate between different closed string configurations via
joining/splitting interactions similar to those of string field theory. We
construct them starting from branched coverings of Riemann surfaces. For the
class of them which we analyze in detail the construction can be made explicit
in terms U(N) affine Toda field theories.Comment: 12 pages, 1 eps figure, JHEP.cls LaTeX2e class file; sign corrected,
ref. and acknowledgements update
Heterotic Matrix String Theory and Riemann Surfaces
We extend the results found for Matrix String Theory to Heterotic Matrix
String Theory, i.e. to a 2d O(N) SYM theory with chiral (anomaly free) matter
and N=(8,0) supersymmetry. We write down the instanton equations for this
theory and solve them explicitly. The solutions are characterized by branched
coverings of the basis cylinder, i.e. by compact Riemann surfaces with
punctures. We show that in the strong coupling limit the action becomes the
heterotic string action plus a free Maxwell action. Moreover the amplitude
based on a Riemann surface with p punctures and h handles is proportional to
g^{2-2h-p}, as expected for the heterotic string interaction theory with string
coupling g_s=1/g.Comment: 17 pages, JHEP LaTeX style, sentence delete
Spherically Symmetric Solutions in Ghost-Free Massive Gravity
Recently, a class of theories of massive gravity has been shown to be
ghost-free. We study the spherically symmetric solutions in the bigravity
formulation of such theories. In general, the solutions admit both a Lorentz
invariant and a Lorentz breaking asymptotically flat behaviour and also fall in
two branches. In the first branch, all solutions can be found analitycally and
are Schwarzschild-like, with no modification as is found for other classes of
theories. In the second branch, exact solutions are hard to find, and relying
on perturbation theory, Yukawa-like modifications of the static potential are
found. The general structure of the solutions suggests that the bigravity
formulation of massive gravity is crucial and more than a tool.Comment: 15 pages. Some change in the reference
Stars and (Furry) Black Holes in Lorentz Breaking Massive Gravity
We study the exact spherically symmetric solutions in a class of
Lorentz-breaking massive gravity theories, using the effective-theory approach
where the graviton mass is generated by the interaction with a suitable set of
Stuckelberg fields. We find explicitly the exact black hole solutions which
generalizes the familiar Schwarzschild one, which shows a non-analytic hair in
the form of a power-like term r^\gamma. For realistic self-gravitating bodies,
we find interesting features, linked to the effective violation of the Gauss
law: i) the total gravitational mass appearing in the standard 1/r term gets a
multiplicative renormalization proportional to the area of the body itself; ii)
the magnitude of the power-like hairy correction is also linked to size of the
body. The novel features can be ascribed to presence of the goldstones fluid
turned on by matter inside the body; its equation of state approaching that of
dark energy near the center. The goldstones fluid also changes the matter
equilibrium pressure, leading to an upper limit for the graviton mass, m <~
10^-28 - 10^29 eV, derived from the largest stable gravitational bound states
in the Universe.Comment: 22 pages, 4 Figures. Final version to be published in PRD. Typos
corrected, comments adde
Exact Spherically Symmetric Solutions in Massive Gravity
A phase of massive gravity free from pathologies can be obtained by coupling
the metric to an additional spin-two field. We study the gravitational field
produced by a static spherically symmetric body, by finding the exact solution
that generalizes the Schwarzschild metric to the case of massive gravity.
Besides the usual 1/r term, the main effects of the new spin-two field are a
shift of the total mass of the body and the presence of a new power-like term,
with sizes determined by the mass and the shape (the radius) of the source.
These modifications, being source dependent, give rise to a dynamical violation
of the Strong Equivalence Principle. Depending on the details of the coupling
of the new field, the power-like term may dominate at large distances or even
in the ultraviolet. The effect persists also when the dynamics of the extra
field is decoupled.Comment: 24 pages, Latex JHEP style, added clarifications. Version accepted in
JHE
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