839 research outputs found

### The quantum Hilbert space of a chiral two-form in d = 5 + 1 dimensions

We consider the quantum theory of a two-form gauge field on a space-time
which is a direct product of time and a spatial manifold, taken to be a compact
five-manifold with no torsion in its cohomology. We show that the Hilbert space
of this non-chiral theory is a certain subspace of a tensor product of two
spaces, that are naturally interpreted as the Hilbert spaces of a chiral and
anti-chiral two-form theory respectively. We also study the observable
operators in the non-chiral theory that correspond to the electric and magnetic
field strengths, the Hamiltonian, and the exponentiated holonomy of the
gauge-field around a spatial two-cycle. All these operators can be decomposed
into contributions pertaining to the chiral and anti-chiral sectors of the
theory.Comment: 15 page

### BPS states in (2,0) theory on R x T5

We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where
the first factor denotes time, and the second factor is a flat spatial
five-torus. In addition to their energy, quantum states are characterized by
their spatial momentum, 't Hooft flux, and $Sp (4)$ $R$-symmetry
representation. The momentum obeys a shifted quantization law determined by the
't Hooft flux. By supersymmetry, the energy is bounded from below by the
magnitude of the momentum. This bound is saturated by BPS states, that are
annihilated by half of the supercharges. The spectrum of such states is
invariant under smooth deformations of the theory, and can thus be studied by
exploiting the interpretation of $(2, 0)$ theory as an ultra-violet completion
of maximally supersymmetric Yang-Mills theory on $R \times T^4$. Our main
example is the $A$-series of $(2,0)$ theories, where such methods allow us to
study the spectrum of BPS states for many values of the momentum and the 't
Hooft flux. In particular, we can describe the $R$-symmetry transformation
properties of these states by determining the image of their $Sp (4)$
representation in a certain quotient of the $Sp (4)$ representation ring.Comment: 22 page

### The partition bundle of type A_{N-1} (2, 0) theory

Six-dimensional (2, 0) theory can be defined on a large class of
six-manifolds endowed with some additional topological and geometric data (i.e.
an orientation, a spin structure, a conformal structure, and an R-symmetry
bundle with connection). We discuss the nature of the object that generalizes
the partition function of a more conventional quantum theory. This object takes
its values in a certain complex vector space, which fits together into the
total space of a complex vector bundle (the `partition bundle') as the data on
the six-manifold is varied in its infinite-dimensional parameter space. In this
context, an important role is played by the middle-dimensional intermediate
Jacobian of the six-manifold endowed with some additional data (i.e. a
symplectic structure, a quadratic form, and a complex structure). We define a
certain hermitian vector bundle over this finite-dimensional parameter space.
The partition bundle is then given by the pullback of the latter bundle by the
map from the parameter space related to the six-manifold to the parameter space
related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference

### Analyticity Properties of Graham-Witten Anomalies

Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies
according to their analytic properties are of type A (coming from
$\delta$-singularities in correlators of several energy-momentum tensors) or of
type B (originating in counterterms which depend logarithmically on a mass
scale). It is argued that all Graham-Witten anomalies can be divided into 2
groups: internal and external, and that all external anomalies are of type B,
whereas among internal anomalies there is one term of type A and all the rest
are of type B. This argument is checked explicitly for the case of a free
scalar field in a 6-dimensional space with a 2-dimensional submanifold.Comment: 2 typos correcte

### Rigid surface operators and S-duality: some proposals

We study surface operators in the N=4 supersymmetric Yang-Mills theories with
gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these
theories have a class of rigid surface operators which are expected to be
related by S-duality. The rigid surface operators are of two types, unipotent
and semisimple. We make explicit proposals for how the S-duality map should act
on unipotent surface operators. We also discuss semisimple surface operators
and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc

### Extended superspace, higher derivatives and SL(2,Z) duality

We consider the low-energy effective action for the Coulomb phase of an N=2 supersymmetric gauge theory with a rank one gauge group. The N = 2 superspace formalism is naturally invariant under an SL(2, {\bf Z}) group of duality transformations, regardless of the form of the action. The leading and next to leading terms in the long distance expansion of the action are given by the holomorphic prepotential and a real analytic function respectively. The latter is shown to be modular invariant with respect to SL(2, {\bf Z})

### BPS surface observables in six-dimensional (2,0) theory

The supergroup OSp(8*|4), which is the superconformal group of (2,0) theory
in six dimensions, is broken to the subgroup OSp(4|2)xOSp(4|2) by demanding the
invariance of a certain product in a superspace with eight bosonic and four
fermionic dimensions. We show that this is consistent with the symmetry
breaking induced by the presence of a flat two-dimensional BPS surface in the
usual (2,0) superspace, which has six bosonic and sixteen fermionic dimensions.Comment: 9 pages, LaTeX. v2: reference adde

### Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groups

The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills
theory on a spatial three-torus contains a certain number of bound states,
characterized by their discrete abelian magnetic and electric 't Hooft fluxes.
At weak coupling, the wave-functions of these states are supported near points
in the moduli space of flat connections where the unbroken gauge group is
semi-simple. The number of such states is related to the number of normalizable
bound states at threshold in the supersymmetric matrix quantum mechanics with
16 supercharges based on this unbroken group. Mathematically, the determination
of the spectrum relies on the classification of almost commuting triples with
semi-simple centralizers. We complete the work begun in a previous paper, by
computing the spectrum of bound states in theories based on the
even-dimensional spin groups and the exceptional groups. The results satisfy
the constraints of S-duality in a rather non-trivial way.Comment: 20 page

### First Law, Counterterms and Kerr-AdS_5 Black Holes

We apply the counterterm subtraction technique to calculate the action and
other quantities for the Kerr--AdS black hole in five dimensions using two
boundary metrics; the Einstein universe and rotating Einstein universe with
arbitrary angular velocity. In both cases, the resulting thermodynamic
quantities satisfy the first law of thermodynamics. We point out that the
reason for the violation of the first law in previous calculations is that the
rotating Einstein universe, used as a boundary metric, was rotating with an
angular velocity that depends on the black hole rotation parameter. Using a new
coordinate system with a boundary metric that has an arbitrary angular
velocity, one can show that the resulting physical quantities satisfy the first
law.Comment: 19 pages, 1 figur

- âŠ