Generalized ADHM equations from marginal deformations in open superstring field theory

Abstract

Working within the framework of both the A ∞ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the D(−1)/D3 system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory. We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons. ArXiv ePrint: 1910.00538 A Spinors in 4d 55 B Conventions for the A ∞ OSFT 56 C Some useful OPE and correlators 58

Localization of effective actions in heterotic string field theory

“…for all i, j, k. The proof of this claim, which proceeds along the lines of [9], is presented in appendix C. Therefore, given (3.19), the cubic potential vanishes…”

“…In deriving the above expression we have also assumed that the OPE {V 1 2 ,1 V 1,1 } is regular in the holomorphic side. This is generically true when the N = 2 decomposition is available (as we are assuming here), see [9] or appendix C for a proof. Notice in particular that if no field is found at those particular singularities in the OPE, then the quartic effective potential is identically vanishing.…”

“…Then, following [11,12], we observe that when the massless fields we are interested in are charged under the R-charge of an underlying N = 2 SCFT in the left-moving sector, the full quartic potential localizes at the boundary of moduli space of the 4-punctured sphere. Although we are here talking about closed string amplitudes, the mechanism is completely parallel to the open string case analyzed in [12] and [9,11].…”

“…Concentrating thus on the ϕ A fields only, we further restrict our attention to N = 1 superconformal primaries which can be written as sum of short N = 2 primaries of R-charge ±1 [9,11,12,38] V j 1 2 (z) = (V j 1 2 ) + (z) + (V j 1 2 ) − (z) (1.6) and accordingly from (1.5)…”

“…with vanishing R-charge. It is important to realize that while in the open string case localization was just a shortcut to a more complicated computation involving (still exactly computable) 4-point OSFT diagrams [9,57], here this is a truly major advantage as it gives us the possibility to access to the full quartic potential without an explicit representation of the fundamental vertices of the microscopic closed string field theory; all complications of closed string field theory have been by-passed. This is the central result of this paper, which is organized as follows.…”