1.
Three-dimensional Quantum Supergravity
and Supersymmetric Spin Foam Models - Livine, Etera R.; Oeckl, Robert
We show how super BF theory in any dimension can be quantized as a
spin foam model, generalizing the situation for ordinary BF theory.
This is a first step toward quantizing supergravity theories.
¶
We investigate in particular 3-dimensional $(p=1,q=1)$
supergravity which we quantize exactly. We obtain a
super-Ponzano-Regge model with gauge group $\OSp(1|2)$.
A main motivation
for our approach is the implementation of fermionic degrees of
freedom in spin foam models.
Indeed, we propose a description of the fermionic
degrees of freedom in our model.
Complementing the path integral approach we also discuss aspects of a
canonical quantization in the spirit of loop quantum gravity.
Finally, we comment on $2\! +\! 1$-dimensional quantum...
2.
The quantisation of Poisson structures arising in
Chern-Simons theory with gauge group $G \ltimes \mathfrac{g}*$ - Meusburger, C.; Schroers, B. J.
We quantise a Poisson structure on $H^{n+2g}$, where
$H$ is a semidirect product group of the form
$G\ltimes\mathfrak{g}^*$.
This Poisson structure
arises in the combinatorial description of the phase space
of Chern-Simons theory with
gauge group $G\ltimes\mathfrak{g}^*$
on $\mathbb{R}\times S_{g,n}$, where $S_{g,n}$ is a surface of genus
$g$ with $n$ punctures. The quantisation of this Poisson structure is
a key step in the quantisation of Chern-Simons theory with gauge group
$G\ltimes\mathfrak{g}^*$.
We construct the quantum algebra and its irreducible
representations and show that the quantum double $D(G)$ of the group
$G$ arises naturally as a symmetry of the quantum algebra.
3.
The Glueball Superpotential - Aganagic, Mina; Intriligator, Ken; Vafa, Cumrun; Warner, Nicholas P.
We compute glueball superpotentials for four-dimensional, ${\cal N}=1$
supersymmetric gauge theories, with arbitrary gauge groups and massive
matter representations. This is done by perturbatively integrating
out massive charged fields. The Feynman diagram computations
simplify, and are related to the corresponding matrix model. This
leads to a natural notion of ``projection to planar diagrams'' for
arbitrary gauge groups and representations. We discuss a general
ambiguity in the glueball superpotential $W(S)$ for terms, $S^n$,
whose order, $n$ is greater than the dual Coxeter number. This
ambiguity can be resolved for all classical gauge groups $(A,B,C,D)$,
via a natural embedding in an infinite rank supergroup. We use this to
resolve some recently raised puzzles....
4.
Virtual class of zero loci and mirror theorems - Elezi, Artur; Luo, Feng
Let $Y$ be the zero loci of a regular section of a
convex vector bundle $E$ over $X$. We provide a proof of a
conjecture of Cox, Katz and Lee for the virtual class of the genus
zero moduli of stable maps to $Y$. This in turn yields the
expected relationship between Gromov-Witten theories of $Y$ and
$X$ which together with Mirror Theorems allows for the calculation
of enumerative invariants of $Y$ inside of $X$.
5.
Large Volume Perspective on Branes at Singularities - Wijnholt, Martijn
In this paper we consider a somewhat unconventional approach for
deriving worldvolume theories for D3 branes probing Calabi-Yau singularities.
The strategy consists of extrapolating the calculation of F-terms
to the large volume limit. This method circumvents the inherent limitations
of more traditional approaches used for orbifold and toric singularities.
We illustrate its usefulness by
deriving quiver theories for D3 branes probing singularities where
a Del Pezzo surface containing four, five or six exceptional curves
collapses to zero size. In the latter two cases the superpotential
depends explicitly on complex structure parameters.
These are examples of probe theories for singularities which can
currently not be computed by other means.
6.
Matrix Models and Gravitational Corrections - Dijkgraaf, Robbert; Sinkovics, Annamaria; Tem, Mine
We provide evidence of the relation between supersymmetric gauge
theories and matrix models beyond the planar limit. We compute
gravitational $R^2$ couplings in gauge theories perturbatively, by
summing genus one matrix model diagrams. These diagrams give the
leading $1/N^2$ corrections in the large $N$ limit of the matrix model
and can be related to twist field correlators in a collective
conformal field theory. In the case of softly broken $SU(N)\ \cN=2$
super Yang-Mills theories, we find that these exact solutions of the
matrix models agree with results obtained by topological field theory
methods.
7.
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory - Landi, Giovanni; Lizzi, Fedele; Szabo, Richard J.
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.
8.
The Trautman-Bondi mass of hyperboloidal initial data sets - Chru?ciel, Piotr T.; Jezierski, Jacek; ??ski, Szymon
We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the resulting mass is a geometric invariant, and we prove positivity thereof in the case of a spherical conformal infinity. When R(g) -- or, equivalently, trgK -- tends to a negative constant to order one at infinity, the definition is expressed purely in terms of three-dimensional or two-dimensional objects.
9.
Effective Superpotentials, Geometry and Integrable Systems - Kennaway, Kristian D.; Warner, Nicholas P.
We consider the effective superpotentials of N; = 1 SU(Nc) and U(Nc) supersymmetric gauge theories that are obtained from the N = 2 theory by adding a tree-level superpotential. We show that several of the techniques for computing the effective superpotential are implicitly regularized by 2Nc massive chiral multiplets in the fundamental representation, i.e. the gauge theory is embedded in the finite theory with nontrivial UV fixed point. In the maximally confining phase we obtain explicit general formulae for the effective superpotential, which reduce to previously known results in particular cases. In order to study N = 1 and N...
10.
Matroids and p-Branes - Nieto, J. A.
A link between matroid theory and p-branes is discussed. The Schild type action for p-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to p-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory.
11.
On quantum symmetries of ADE graphs - Coquereaux, Robert; Trinchero, Roberto
The double triangle algebra (DTA) associated to an ADE graph is considered. A description of its bialgebra structure based on a reconstruction approach is given. This approach takes as initial data the representation theory of the DTA as given by Ocneanu's cell calculus. It is also proved that the resulting DTA has the structure of a weak *-Hopf algebra. As an illustrative example, the case of the graph A3 isdescribed in detail.
12.
Supersymmetric Kaluza-Klein reductions of AdS backgrounds - Figueroa-O'Farrill, José; Simón, Joan
This paper contains a classification of smooth Kaluza-Klein reductions (by one-parameter subgroups) of the maximally supersymmetric anti de Sitter backgrounds of supergravity theories. We present a classification of one-parameter subgroups of isometries of anti de Sitter spaces, discuss the causal properties of their orbits on these manifolds, and discuss their action on the space of Killing spinors. We analyse the problem of which quotients admit a spin structure. We then apply these results to write down the list of smooth everywhere spacelike supersymmetric quotients of AdS3 x S3(x ?4), AdS4 x S7, AdS5 x S5 and AdS7 x S4, and...
13.
Transition from big crunch to big bang in brane cosmology - Gerhardt, Claus
We consider branes N = I x S0, where S0 is an n-dimensional space form, not necessarily compact, in a Schwarzschild-AdS(n+2) bulk N. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the singularity to a reflected brane \hat N, which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS(n+2) bulk \hat N . The joint branes N ? \hat N can thus be naturally embedded in ?2 x S0, hence there exists a second...
14.
M-theory, type IIA superstrings, and elliptic cohomology - Kriz, Igor; Sati, Hisham
The topological part of the M-theory partition function was shown by Witten to be encoded in the index of an E8 bundle in eleven dimensions. This partition function is, however, not automatically anomalyfree. We observe here that the vanishing W7 = 0 of the Diaconescu-Moore-Witten anomaly [1] in IIA and compactified M-theory partition function is equivalent to orientability of spacetime with respect to (complex-oriented) elliptic cohomology. Motivated by this, we define an elliptic cohomology correction to the IIA partition function, and propose its relationship to interaction between 2- and 5-branes in the M-theory limit.
15.
Limiting behavior of local
Calabi-Yau metrics - Zharkov
, Ilia
We use a generalization of the Gibbons-Hawking ansatz to study
the behavior of certain non-compact Calabi-Yau manifolds in the large
complex structure limit. This analysis provides an intermediate step
toward proving the metric collapse conjecture for toric hypersurfaces
and complete intersections.
16.
Effective Stringy Description of
Schwarzschild Black Holes - Krasnov
, Kirill; Solodukhin
, Sergey N.
We start by pointing out that certain Riemann surfaces appear
rather naturally in the context of wave equations in the black hole background.
For a given black hole there are two closely related surfaces.
One is the Riemann surface of complexified "tortoise" coordinate. The
other Riemann surface appears when the radial wave equation is interpreted
as the Fuchsian differential equation. We study these surfaces
in detail for the BTZ and Schwarzschild black holes in four and higher
dimensions. Topologically, in all cases both surfaces are a sphere with a
set of marked points; for BTZ and 4D Schwarzschild black holes there
is 3 marked points. In certain limits the...
17.
Fractional Branes in
Landau-Ginzburg Orbifolds - Ashok
, S.K.; Dell'Aquila
, E.; Diaconescu
, D.-E.
We construct fractional branes in Landau-Ginzburg orbifold categories
and study their behavior under marginal closed string perturbations.
This approach is shown to be more general than the rational
boundary state construction. In particular we find new D-branes on
the quintic -- such as a single D0-brane -- which are not restrictions
of bundles on the ambient projective space. We also exhibit a family
of deformations of the D0-brane in the Landau-Ginzburg category
parameterized by points on the Fermat quintic.
18.
Obstructed D-Branes in
Landau-Ginzburg Orbifolds - Ashok
, S.K.; Dell'Aquila
, E.; Diaconescu
, D.-E.; Florea
, B.
We study deformations of Landau-Ginzburg D-branes corresponding
to obstructed rational curves on Calabi-Yau threefolds. We determine
D-brane moduli spaces and D-brane superpotentials by evaluating
higher products up to homotopy in the Landau-Ginzburg orbifold category.
For concreteness we work out the details for lines on a perturbed
Fermat quintic. In this case we show that our results reproduce the
local analytic structure of the Hilbert scheme of curves on the threefold.
19.
Covariant Hamiltonian formalism
for the calculus of variations with
several variables: Lepage-Dedecker
versus De Donder-Weyl - Hélein
, Frédéric; Kouneiher
, Joseph
The main purpose in the present paper is to build a Hamiltonian
theory for fields which is consistent with the principles of relativity.
For this we consider detailed geometric pictures of Lepage theories in
the spirit of Dedecker and try to stress out the interplay between the
Lepage-Dedecker (LP) description and the (more usual) De Donder-
Weyl (DDW) one. One of the main points is the fact that the Legendre
transform in the DDW approach is replaced by a Legendre correspondence
in the LP theory (this correspondence behaves differently:
ignoring the singularities whenever the Lagrangian is degenerate).
20.
Comments on N = 1 Heterotic String Vacua - Andreas, B.; Hernandez Ruiperez, D.
We analyze three aspects of N = 1 heterotic string compactifications
on elliptically fibered Calabi-Yau threefolds:
stability of vector bundles, five-brane instanton transitions and chiral matter.
First we show that relative Fourier-Mukai transformation preserves absolute stability.
This is relevant for vector bundles whose spectral cover is reducible. Then we
derive an explicit formula for the number of moduli which occur in (vertical)
five-brane instanton transitions provided a certain vanishing argument
applies. Such transitions increase the holonomy of the heterotic vector
bundle and cause gauge changing phase transitions.
In a M-theory description the transitions are associated with collisions of bulk
five-branes with one of the boundary fixed planes.
In F-theory they correspond...
1.
