Twistor superstring in two-time physics

Abstract

By utilizing the gauge symmetries of two-time physics (2T physics), a superstring with linearly realized global $\mathrm{S}\mathrm{U}(2,2|4)$ supersymmetry in $4+2$ dimensions (plus internal degrees of freedom) is constructed. It is shown that the dynamics of the Witten-Berkovits twistor superstring in $3+1$ dimensions emerges as one of the many one-time (1T) holographic pictures of the $4+2$ dimensional string obtained via gauge fixing of the 2T gauge symmetries. In 2T physics the twistor language can be transformed to usual spacetime language and vice versa, off shell, as different gauge fixings of the same 2T string theory. Further holographic string pictures in $3+1$ dimensions that are dual theories also can be derived. The 2T superstring is further generalized in the $\mathrm{S}\mathrm{U}(4)=\mathrm{S}\mathrm{O}(6)$ sector of $\mathrm{S}\mathrm{U}(2,2|4)$ by the addition of six bosonic dimensions, for a total of $10+2$ dimensions. Excitations of the extra bosons produce a $\mathrm{S}\mathrm{U}(2,2|4)$ current algebra spectrum that matches the classification of the high-spin currents of $N=4,$ $d=4$ super Yang-Mills theory which are conserved in the weak coupling limit. This spectrum is interpreted as the extension of the $\mathrm{S}\mathrm{U}(2,2|4)$ classification of the Kaluza-Klein towers of typeII-B supergravity compactified on ${\mathrm{A}\mathrm{d}\mathrm{S}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$, into the full string theory, and is speculated to have a covariant $10+2$ origin in F-theory or S-theory. Further generalizations of the superstring theory to $3+2$, $5+2$, and $6+2$ dimensions based on the supergroups $\mathrm{O}\mathrm{S}\mathrm{p}(8|4),$ F(4), $\mathrm{O}\mathrm{S}\mathrm{p}({8}^{*}|4)$, respectively, and other cases, are discussed also. The $\mathrm{O}\mathrm{S}\mathrm{p}({8}^{*}|4)$ case in $6+2$ dimensions can be gauge fixed to $5+1$ dimensions to provide a formulation of the special superconformal theory in six dimensions either in terms of ordinary spacetime or in terms of twistors.