Four-dimensional string/ string/ string triality

Abstract

In six spacetime dimensions, the heterotic string is dual to a Type IIA string. On further toroidal compactification to four spacetime dimensions, the heterotic string acquires an SL(2, Z) S strong/weak coupling duality and an SL(2, Z) T × SL(2, Z) U target space duality acting on the dilaton/axion, complex Kahler form and the complex structure fields S, T, U respectively. Strong/weak duality in D = 6 interchanges the roles of S and T in D = 4 yielding a Type IIA string with fields T, S, U. This suggests the existence of a third string (whose six-dimensional interpretation is more obscure) that interchanges the roles of S and U. It corresponds in fact to a Type IIB string with fields U, T, S leading to a fourdimensional string/string/string triality. Since SL(2, Z) S is perturbative for the Type IIB string, this D = 4 triality implies S-duality for the heterotic string and thus fills a gap left by D = 6 duality. For all three strings the total symmetry is SL(2, Z) S × O(6, 22; Z) T U . The O(6, 22; Z) is perturbative for the heterotic string but contains the conjectured nonperturbative SL(2, Z) X , where X is the complex scalar of the D = 10 Type IIB string. Thus four-dimensional triality also provides a (post-compactification) justification for this conjecture. We interpret the N = 4 Bogomol'nyi spectrum from all three points of view. In particular we generalize the Sen-Schwarz formula for short multiplets to include intermediate multiplets also and discuss the corresponding black hole spectrum both for the N = 4 theory and for a truncated S-T -U symmetric N = 2 theory. Just as the first two strings are described by the four-dimensional elementary and dual solitonic solutions, so the third string is described by the stringy cosmic string solution. In three dimensions all three strings are related by O(8, 24; Z) transformations.

An inverse scattering formalism for STU supergravity

“…The poles at t = − 1 t k come from the factor A + and so we assume this matrix to be of the form 15) and…”

U-invariants, black-hole entropy and fixed scalars

“…The first can be achieved in heterotic or Type II string, with M 4 = T 6 in heterotic and M 4 = K 3 × T 2 in Type II theory. These theories are known to be dual at a non perturbative level [18], [19], [20]. N = 8 corresponds to M 8 = T 6 in Type II.…”

Pair production of small black holes in heterotic string theories

“…1.2 1/2 BPS states with Q 2 = −2, 0 1/2 BPS states with Q 2 = −2 have N R = 0 and are the only states that can lead to gauge symmetry enhancement [54,55,30,31]. Since Q = (n, m, r) = 0, these states are generically massive as M 2 BP S = |p L | 2 ≥ 0.…”