3,703 research outputs found
On the gl(1|1) Wess-Zumino-Witten Model
We continue the study of the gl(1|1) Wess-Zumino-Witten model. The
Knizhnik-Zamolodchikov equations for the one, two, three and four point
functions are analyzed, for vertex operators corresponding to typical and
projective representations. We illustrate their interplay with the logarithmic
global conformal Ward identities. We compute the four point function for one
projective and three typical representations. Three coupled first order
Knizhnik-Zamolodchikov equations are integrated consecutively in terms of
generalized hypergeometric functions, and we assemble the solutions into a
local correlator. Moreover, we prove crossing symmetry of the four point
function of four typical representations at generic momenta. Throughout, the
map between the gl(1|1) Wess-Zumino-Witten model and symplectic fermions is
exploited and extended.Comment: 37 page
An Elliptic Triptych
We clarify three aspects of non-compact elliptic genera. Firstly, we give a
path integral derivation of the elliptic genus of the cigar conformal field
theory from its non-linear sigma-model description. The result is a manifestly
modular sum over a lattice. Secondly, we discuss supersymmetric quantum
mechanics with a continuous spectrum. We regulate the theory and analyze the
dependence on the temperature of the trace weighted by the fermion number. The
dependence is dictated by the regulator. From a detailed analysis of the
dependence on the infrared boundary conditions, we argue that in non-compact
elliptic genera right-moving supersymmetry combined with modular covariance is
anomalous. Thirdly, we further clarify the relation between the flat space
elliptic genus and the infinite level limit of the cigar elliptic genus.Comment: 22 page
Higgsed antisymmetric tensors and topological defects
We find topological defect solutions to the equations of motion of a
generalised Higgs model with antisymmetric tensor fields. These solutions are
direct higher dimensional analogues of the Nielsen-Olesen vortex solution for a
gauge field in four dimensions.Comment: 9 pages, final versio
Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
We study complexified elliptic Calogero-Moser integrable systems. We
determine the value of the potential at isolated extrema, as a function of the
modular parameter of the torus on which the integrable system lives. We
calculate the extrema for low rank B,C,D root systems using a mix of analytical
and numerical tools. For so(5) we find convincing evidence that the extrema
constitute a vector valued modular form for a congruence subgroup of the
modular group. For so(7) and so(8), the extrema split into two sets. One set
contains extrema that make up vector valued modular forms for congruence
subgroups, and a second set contains extrema that exhibit monodromies around
points in the interior of the fundamental domain. The former set can be
described analytically, while for the latter, we provide an analytic value for
the point of monodromy for so(8), as well as extensive numerical predictions
for the Fourier coefficients of the extrema. Our results on the extrema provide
a rationale for integrality properties observed in integrable models, and embed
these into the theory of vector valued modular forms. Moreover, using the data
we gather on the modularity of complexified integrable system extrema, we
analyse the massive vacua of mass deformed N=4 supersymmetric Yang-Mills
theories with low rank gauge group of type B,C and D. We map out their
transformation properties under the infrared electric-magnetic duality group as
well as under triality for N=1* with gauge algebra so(8). We find several
intriguing properties of the quantum gauge theories.Comment: 35 pages, many figure
Schwinger pair production in AdS2
We analyze the pair production of charged particles in two-dimensional
Anti-de Sitter space (AdS_2) with a constant, uniform electric field. We
compute the production rate both at a semi-classical level, viewing Schwinger
pair production as a tunneling event, and at the full quantum level, by
extracting the imaginary part of the one-loop amplitude. In contrast to the
usual Schwinger pair production in flat space, pair production in AdS_2
requires a sufficiently large electric field E^2> M^2+1/4 in order to overcome
the confining effect of the AdS geometry -- put in another way, the presence of
an electric field E raises the Breitenlohner-Freedman bound to M^2 > -1/4 +
E^2. For E greater than this threshold, the vacuum is unstable to production of
charged pairs in the bulk. We expect our results to be helpful in constructing
supersymmetric AdS_2 X S^2 perturbative string vacua, which enter in the
near-horizon limit of extremal charged black holes. Although the generalized
Breitenlohner-Freedman bound is obeyed in these cases, production of BPS
particles at threshold is possible and relevant for AdS_2 fragmentation.Comment: 23 pages, 4 figures, v2:important revision, discussion of one-loop
amplitude extended, several references adde
Permutations of Massive Vacua
We discuss the permutation group G of massive vacua of four-dimensional gauge
theories with N=1 supersymmetry that arises upon tracing loops in the space of
couplings. We concentrate on superconformal N=4 and N=2 theories with N=1
supersymmetry preserving mass deformations. The permutation group G of massive
vacua is the Galois group of characteristic polynomials for the vacuum
expectation values of chiral observables. We provide various techniques to
effectively compute characteristic polynomials in given theories, and we deduce
the existence of varying symmetry breaking patterns of the duality group
depending on the gauge algebra and matter content of the theory. Our examples
give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur
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