1,546 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 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
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 low-energy spectrum of (2,0) theory on T^5 x R
We consider the ADE-series of (2, 0) supersymmetric quantum theories on T^5
\times R, where the first factor is a flat spatial five-torus, and the second
factor denotes time. The quantum states of such a theory \Phi are characterized
by a discrete quantum number f \in H^3 (T^5, C), where the finite abelian group
C is the center subgroup of the corresponding simply connected simply laced Lie
group G. At energies that are low compared to the inverse size of the T^5, the
spectrum consists of a set of continua of states, each of which is
characterized by the value of f and some number 5r of additional continuous
parameters. By exploiting the interpretation of this theory as the ultraviolet
completion of maximally supersymmetric Yang-Mills theory on T^4 \times S^1
\times R with gauge group G_{adj} = G/C and coupling constant g given by the
square root of the radius of the S^1 factor, one may compute the number N_f^r
(\Phi) of such continua. We perform these calculations in detail for the A- and
D-series. While the Yang-Mills theory formalism is manifestly invariant under
the \SL_4 (Z) mapping class group of T^4, the results are actually found to be
invariant under the \SL_5 (Z) mapping class group of T^5, which provides a
strong consistency check.Comment: 33 page
Commutation relations for surface operators in six-dimensional (2, 0) theory
The A_{N - 1} (2, 0) superconformal theory has an observable associated with
every two-cycle in six dimensions. We make a natural guess for the commutation
relations of these operators, which reduces to the commutation relations of
Wilson and 't Hooft lines in four-dimensional SU(N) N = 4 super Yang-Mills
theory upon compactification on a two-torus. We then verify these commutation
relations by considering the theory at a generic point of its moduli space and
including in the surface operators only contributions from the light degrees of
freedom, which amount to N - 1 (2, 0) tensor multiplets.Comment: 7 page
Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theory
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons
term on a flat spatial two-torus in the limit when the torus becomes small. The
zero-modes of the fields then decouple from the non-zero modes and give rise to
a spectrum of states with energies that are given by multiples of the square of
the coupling constant. We discuss the determination of this low-energy
spectrum, both for simply connected gauge groups and for gauge groups of
adjoint type, with a few examples worked out in detail.Comment: 13 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
Weyl anomaly for Wilson surfaces
We consider a free two-form in six dimensions and calculate the conformal
anomaly associated with a Wilson surface observable.Comment: 8 page
A short representation of the six-dimensional (2, 0) algebra
We construct a BPS-saturated representation of the six-dimensional (2, 0)
algebra with a certain non-zero value of the `central' charge. This
representation is naturally carried by strings with internal degrees of freedom
rather than by point particles. Upon compactification on a circle, it reduces
to a massive vector multiplet in five dimensions. We also construct quantum
fields out of the creation and annihilation operators of the states of this
representation, and show how they give rise to a conserved two-form current
that can be coupled to a tensor multiplet. We hope that these results may be
relevant for understanding the degrees of freedom associated with strings in
interacting (2, 0) theories.Comment: 11 page
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