Unity of superstring dualities

Abstract

The effective action for type II string theory compactified on a six torus is N = 8 supergravity, which is known to have an E 7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 (Z), which contains both the T-duality group O(6, 6; Z) and the S-duality group SL(2; Z). We present evidence for the conjecture that E 7 (Z) is an exact 'U-duality' symmetry of type II string theory. This conjecture requires certain extreme black hole states to be identified with massive modes of the fundamental string. The gauge bosons from the Ramond-Ramond sector couple not to string excitations but to solitons. We discuss similar issues in the context of toroidal string compactifications to other dimensions, compactifications of the type II string on K 3 ×T 2 and compactifications of eleven-dimensional supermembrane theory.

Curvatures and potential of M–theory inD= 4 with fluxes and twist

“…The C 0ij fields give masses to the A ij vector fields with the exception of the three entries (ij) = (1, 2), (3,4), (5,6). Therefore three of the C 0ij scalar remain massless moduli.…”

New “gauge” theories in six dimensions

“…Now make a T-duality transformation, on the F orbits, to convert to a Type IIB description. The T-duality converts Kaluza-Klein monopoles to NS fivebranes, as one can see by looking at how T-duality acts on the fields that the monopoles and fivebranes create at infinity [14]. 5 So the Type IIB dual of the multi-Kaluza-Klein monopole solution is a configuration of q NS fivebranes on E 3 x S 1 .…”

“…In fact, modulo inner automorphisms (which correspond to turning on Wilson lines), it is the unique outer automorphism of SU(2k -4); it acts by charge conjugation, and will be called When an SU(2k -4) group element g is transported around the S 1 , it returns to ^(g) =g if there is no Wilson line on the S 1 . If on the other hand there is a Wilson line corresponding to an element a G SU(2k -4), 14 then the monodromy is g -> agoT 1 . The unbroken gauge group consists of group elements such that g = agar l .…”

Non-planar string networks on tori

“…Classification of type II BPS states with different supersymmetries have been discussed in several papers [1,2]. They form U-duality multiplets of stings in various dimensions.…”

“…and two other expressions obtained by taking cyclic permutations in indices (1,2,3) and (p, q, r). Similarly,…”