Multiloop amplitudes of light-cone gauge NSR string field theory in noncritical dimensions

Abstract

Feynman amplitudes of light-cone gauge superstring field theory are ill-defined because of various divergences. In a previous paper, one of the authors showed that taking the worldsheet theory to be the one in a linear dilaton background Φ = −iQX 1 with Feynman iε (ε > 0) and Q 2 > 10 yields finite amplitudes. In this paper, we apply this worldsheet theory to dimensional regularization of the light-cone gauge NSR superstring field theory. We concentrate on the amplitudes for even spin structure with external lines in the (NS,NS) sector. We show that the multiloop amplitudes are indeed regularized in our scheme and that they coincide with the results in the first-quantized formalism through the analytic continuation Q → 0.

Multiloop amplitudes of light-cone gauge superstring field theory: odd spin structure contributions

“…Although Lorentz invariance is broken by doing so, it does not cause so much trouble because the light-cone gauge theory is a completely gauge-fixed theory. In [13], we have shown that the multiloop amplitudes corresponding to the Riemann surfaces with even spin structure involving external lines in the (NS,NS) sector can be calculated using the dimensional regularization and the results coincide with those of the first-quantized approach.…”

“…B and F denote the sums over bosonic and fermionic string fields respectively. The three-string vertices V 3 | are elements of H * ⊗ H * ⊗ H * whose definition can be found in [13,15,16]. Here H * denotes the dual space of H.…”

“…S LC X i , ψ i ,ψ i denotes the worldsheet action of the transverse variables and the path integral measure dX i dψ i dψ i ĝzz is defined with the metric dŝ 2 = 2ĝ zz dzdz. Since the integrand was defined by using the metric (2.7), we need the anomaly factor e − 1 2 Γ[σ;ĝzz] , where As was demonstrated in [13], if all the external lines are in the (NS,NS) sector and the spin structure for the left and right fermions are both even, the term in the sum in (2.8) can be recast into a conformal gauge expression:…”

“…The proof was formal because there appear unphysical divergences which are called the contact term divergences [8][9][10][11][12]. In a previous paper [13], we have shown that these divergences can be dealt with by dimensional regularization. In the case of type II superstrings, for example, one formulates a light-cone gauge superstring field theory in noncritical dimensions or the one whose worldsheet theory for transverse variables is a superconformal field theory with central charge c = 12 [14].…”

“…The organization of this paper is as follows. In section 2, we review the results in [13] and the problems with the odd spin structures. In section 3, we deal with the amplitudes for the odd spin structure and show that these also coincide with those from the first-quantized approach.…”