# Theoretical High Energy Seminar – Niels Bohr Institute - University of Copenhagen

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# Theoretical High Energy Seminar

Koichi Murakami (Okayama Institute for Quantum Physics)

Title: Light-cone gauge superstring theory and dimensional regularisation

Abstract:
We propose a dimensional regularization scheme to deal with the divergences  caused by colliding supercurrents inserted at the interaction points, in  the light-cone gauge NSR closed superstring field theory. In this scheme, we formulate the theory in $d$ dimensional spacetime and  define the amplitudes as analytic functions of $d$. We show that by  considering $d$ to be largely negative, the divergences of the theory  are indeed regularized.   In the conformal gauge, this regularized string theory in noncritical  $d$ dimensions corresponds to worldsheet theory with nonstandard  longitudinal part. We formulate this longitudinal part as an interacting CFT with right value of the Virasoro central charge,  so that a nilpotent BRST charge can be constructed with the transverse part and the reparametrization ghosts incorporated.

Using this CFT, we show that the tree level amplitudes for  the (NS,NS) strings of the light-cone gauge superstring field theory in  noncritical dimensions can be recast into a BRST invariant form. We also show that in the limit $d \to 10$ they coincide with the results of the first quantized theory without adding any contact interaction terms to the action.

If I have a time at the seminar, I will also discuss the application of our scheme to the Ramond sector and to loop amplitudes.