The low-energy spectrum of (2,0) theory on T5 x R

Journal article, 2008

We consider the ADE-series of (2, 0) supersymmetric quantum theories on T(5) x 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 is an element of 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 T5, 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) x S(1) x 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.