An SL(2, Z) multiplet of type IIB super five-branes

Abstract

It is well-known that the low energy string theory admits a non-singular solitonic super five-brane solution which is the magnetic dual to the fundamental string solution. By using the symmetry of the type IIB string theory, we construct an SL(2, Z) multiplet of magnetically charged super five-branes starting from this solitonic solution. These solutions are characterized by two integral three-form charges (q 1 , q 2 ) and are stable when the integers are coprime. We obtain an expression for the tension of these (q 1 , q 2 ) five-branes as envisaged by Witten. The SL(2, Z) multiplets of black strings and black fivebranes and the existence of similar magnetic dual solutions of strings in type II string theory in D < 10 have also been discussed. .in * Earlier attempt for the construction of SL(2, Z) multiplet of five-brane solution of type IIB string theory were made in [13,14], but the solutions described there are incomplete.

Type IIB 7-branes in warped AdS6: partition functions, brane webs and probe limit

“…Combined with the observation that at each pole p m the solution turns into a (q 1 , q 2 )Q 5-brane solution, in the conventions of [23], with 15) this gives a direct identification of the supergravity solutions with 5-brane intersections.…”

“…The differentials of these functions have common poles on the boundary of Σ, at which the entire solution approaches that for a (p, q) 5-brane, as constructed in [23], with p − iq identified with the residue at the pole. This facilitates the identification of the solutions with (p, q) 5-brane webs.…”

(m, n)-String in (p, q)-string and (p, q)-five-brane background

“…Such a procea e-mail: klu@physics.muni.cz dure was first used in a famous paper [7] where the manifestly SL(2, R) covariant supergravity solution corresponding to a ( p, q)-string was found. The extension of this analysis to the case of an NS5-brane was performed in [8] when the SL(2, Z ) covariant expression for supergravity solutions corresponding to the ( p, q)-five brane was derived. 1 These backgrounds are very interesting and certainly deserve to be studied further.…”

“…However, the fact that the ( p, q) string has to map to another ( p , q )-string where p , q are integers suggests that the full symmetry group of the combined action breaks to SL (2, Z ). On the other hand, solutions found in [7,8] were determined using the SL(2, R) matrices so that it is interesting to analyze the problem of an (m, n)-string probe in such a background and this is precisely the aim of this paper.…”

“…This problem is currently under study and we return to it in the near future. We rather focus on the dynamics of the probe (m, n)-string in the backgrounds [7,8], following the very nice analysis introduced in [14]. Using a manifest SL(2, Z ) covariant formulation of a probe (m, n)-string we can analyze the time evolution of the homogeneous time-dependent string in a given background.…”