SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

Abstract

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

“…As discussed in [10][11][12], various correlation functions of the two-dimensional type IIA superstring theory compactified on R × S 1 at the selfdual radius, with the string coupling g s and the Liouville coupling ω (multiplied by the tachyon operator), coincide with their counterparts in this matrix model through the identification g s = N −1 and 4ω = µ 2 − 2, in the double scaling limit…”

“…Using this expression, one-and two-instanton effects to the one-point function and Z (1,0) (µ 2 ) are analytically obtained in [12], from which spontaneous breaking of SUSY by instantons is concluded. Full nonperturbative contributions are also numerically computed up to N = 10 6 , and these results are extrapolated to N = ∞.…”

“…The issue of the analyticity is discussed in section 4 of [45]. Although the fact of the SUSY breaking has been observed analytically from the one-or two-instanton contributions and numerically as well in [12], the region s > 0 is focused there. Thus, our finding of the full nonperturbative free energy valid for s ∈ (−∞, ∞) provides a new insight into the analytic structure of the IIA superstring theory.…”

“…(5.26), (5.31) of ref. [12] derived directly from the properties of the Hermite polynomials. 9 Note that asymptotic expansion of the Airy function consists of a single exponential [46] Ai…”

“…In this situation, a simple double-well SUSY matrix model had been recently considered in [7,8], and its connection to two-dimensional type IIA superstring theory [9] on a nontrivial Ramond-Ramond background had been explored from the viewpoint of symmetries [10] and from direct comparison of scattering amplitudes at the tree and one-loop orders [11]. Interestingly, in a double scaling limit that realizes the type IIA superstring theory, instanton effects of the matrix model survive and break the SUSY spontaneously [12]. This suggests that the corresponding type IIA superstring theory nonperturbatively breaks its target-space SUSY.…”