12 research outputs found
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
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
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
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
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
Tunneling solutions in topological field theory on R x S^3 x I
We consider a topologically twisted version, recently introduced by Witten,
of five-dimensional maximally supersymmetric Yang-Mills theory on a
five-manifold of the form M_5 =R x W_3 x I. If the length of the interval I is
sufficiently large, the supersymmetric localization equations admit pairs of
static solutions (with the factor R interpreted as Euclidean time). However,
these solutions disappear for a sufficiently short I, so by the topological
invariance of the theory, they must be connected by an interpolating dynamic
instanton solution. We study this for the case that W_3 is a three-sphere S^3
with the standard metric by making a spherically symmetric Ansatz for all
fields. The solution is given as a power series in a parameter related to the
length of I, and we give explicit expressions for the first non-trivial terms.Comment: Added paragraph on instanton numbe
Supersymmetric coupling of a self-dual string to a (2,0) tensor multiplet background
We construct an interaction between a (2,0) tensor multiplet in six
dimensions and a self-dual string. The interaction is a sum of a Nambu-Goto
term, with the tension of the string given by the modulus of the scalar fields
of the tensor multiplet, and a non-local Wess-Zumino term, that encodes the
electromagnetic coupling of the string to the two-form gauge field of the
tensor multiplet. The interaction is invariant under global (2,0)
supersymmetry, modulo the equations of motion of a free tensor multiplet. It is
also invariant under a local fermionic kappa-symmetry, as required by the
BPS-property of the string.Comment: 12 pages, LaTe
Special Geometry and Automorphic Forms
We consider special geometry of the vector multiplet moduli space in
compactifications of the heterotic string on or the type IIA
string on -fibered Calabi-Yau threefolds. In particular, we construct a
modified dilaton that is invariant under T-duality
transformations at the non-perturbative level and regular everywhere on the
moduli space. The invariant dilaton, together with a set of other coordinates
that transform covariantly under , parameterize the moduli space.
The construction involves a meromorphic automorphic function of ,
that also depends on the invariant dilaton. In the weak coupling limit, the
divisor of this automorphic form is an integer linear combination of the
rational quadratic divisors where the gauge symmetry is enhanced classically.
We also show how the non-perturbative prepotential can be expressed in terms of
meromorphic automorphic forms, by expanding a T-duality invariant quantity both
in terms of the standard special coordinates and in terms of the invariant
dilaton and the covariant coordinates.Comment: 21 pages, plain LaTeX. Minor changes, references adde