12 research outputs found

    Commutation relations for surface operators in six-dimensional (2, 0) theory

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    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

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    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

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    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

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    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

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    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

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    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

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    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

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    We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on K3Ă—T2K3 \times T^2 or the type IIA string on K3K3-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under SO(2,n;Z)SO(2, n; Z) 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 SO(2,n;Z)SO(2, n; Z), parameterize the moduli space. The construction involves a meromorphic automorphic function of SO(2,n;Z)SO(2, n; Z), 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
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