41 research outputs found
Duality of string amplitudes in a curved background
We initiate a program to study the relationship between the target space, the
spectrum and the scattering amplitudes in string theory. We consider scattering
amplitudes following from string theory and quantum field theory on a curved
target space, which is taken to be the group manifold, with special
attention given to the duality between contributions from different channels.
We give a simple example of the equivalence between amplitudes coming from
string theory and quantum field theory, and compute the general form of a
four-scalar field theoretical amplitude. The corresponding string theory
calculation is performed for a special case, and we discuss how more general
string theory amplitudes could be evaluated.Comment: 29 page
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
The light spectrum near the Argyres-Douglas point
We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single
quark hypermultiplet in the fundamental representation. For a specific value of
the quark bare mass and at a certain point in the moduli space of vacua, the
central charges corresponding to two mutually non-local electro-magnetic
charges vanish simultaneously, indicating the possibility of massless such
states in the spectrum. By realizing the theory as an M-theory configuration,
we show that these states indeed exist in the spectrum near the critical point.Comment: 7 pages. Late
BPS states in (2,0) theory on R x T5
We consider theory on a space-time of the form , 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 -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 theory as an ultra-violet completion
of maximally supersymmetric Yang-Mills theory on . Our main
example is the -series of 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 -symmetry transformation
properties of these states by determining the image of their
representation in a certain quotient of the representation ring.Comment: 22 page
Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-model
We consider the (2, 0) supersymmetric theory of tensor multiplets and
self-dual strings in six space-time dimensions. Space-time diffeomorphisms that
leave the string world-sheet invariant appear as gauge transformations on the
normal bundle of the world-sheet. The naive invariance of the model under such
transformations is however explicitly broken by anomalies: The electromagnetic
coupling of the string to the two-form gauge field of the tensor multiplet
suffers from a classical anomaly, and there is also a one-loop quantum anomaly
from the chiral fermions on the string world-sheet. Both of these contributions
are proportional to the Euler class of the normal bundle of the string
world-sheet, and consistency of the model requires that they cancel. This
imposes strong constraints on possible models, which are found to obey an
ADE-classification. We then consider the decoupled world-sheet theory that
describes low-energy fluctuations (compared to the scale set by the string
tension) around a configuration with a static, straight string. The anomaly
structure determines this to be a supersymmetric version of the level one
Wess-Zumino-Witten model based on the group (R x SU(2))/Z_2 .Comment: 14 pages. Further clarifications and references adde
Boundary conditions for GL-twisted N=4 SYM
We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a
four-manifold of the form V = W \times R_+ or V = W \times I, where W is a
Riemannian three-manifold. Different kinds of boundary conditions apply at
infinity or at finite distance. We verify that each of these conditions defines
a `middle-dimensional' subspace of the space of all bulk solutions. Taking the
two boundaries of V into account should thus generically give a discrete set of
solutions. We explicitly find the spherically symmetric solutions when W = S^3
endowed with the standard metric. For widely separated boundaries, these
consist of a pair of solutions which coincide for a certain critical value of
the boundary separation and disappear for even smaller separations.Comment: 14 pages, 1 figure, minor change
Dyonic Anomalies
We consider the problem of coupling a dyonic p-brane in d = 2p+4 space-time
dimensions to a prescribed (p+2)-form field strength. This is particularly
subtle when p is odd. For the case p = 1, we explicitly construct a coupling
functional, which is a sum of two terms: one which is linear in the prescribed
field strength, and one which describes the coupling of the brane to its
self-field and takes the form of a Wess-Zumino term depending only on the
embedding of the brane world-volume into space-time. We then show that this
functional is well-defined only modulo a certain anomaly, related to the Euler
class of the normal bundle of the brane world-volume.Comment: 7 pages; reference adde
't Hooft Operators in the Boundary
We consider a topologically twisted maximally supersymmetric Yang-Mills
theory on a four-manifold of the form . 't Hooft
disorder operators localized in the boundary component at finite distance of
are relevant for the study of knot theory on the three-manifold , and
have recently been constructed for a gauge group of rank one. We extend this
construction to an arbitrary gauge group . For certain values of the
magnetic charge of the 't Hooft operator, the solutions are obtained by
embedding the rank one solutions in and can be given in closed form.Comment: 9 page