arXiv subjects
Publications and source records attributed to J. S. Bhattacharyya.
We consider the RNS model from a new angle. The longitudinal and time components of the world-sheet fermions add a $U(1)$ charge to a state. Unlike the gauginos, the ground state fermions in the open string sector are complex; spinor representations of $SU(3)_C\otimes SU(2)_L\otimes U(1)_{Y_W}$.
Redefining the vacuum state of a free two-fold $N=1$ covariant supersymmetric string action as the one with all the excited states of world-sheet fermions occupied, makes the theory anomaly free in (3+1)+4 dimensions. While in the $NS$ sector the spectrum resembles the same for the standard $N=1$ superstring theory with one of the $N$ species in the background, in the $R$ sector both the species of fermions are required to describe the relevant spin operators to describe the fermion spectra. A crucial difference from the $D=10, N=1$ theory is that the fermions states are Dirac particles instead of Majorana-Weyl. Even though the full spectrum of the theory contains both bosons and fermions of various spin, there is no space-time supersymmetry due to obvious lack of triality. The four coordinates of the 4 dimensional Euclidean space describes a $CP^2$ to define the confined gauge symmetry $SU(3)_C$. The bosonization of their supersymmetric partners yields additional two coordinates to describe a $S^2$ that defines the $SU(2)_L$ of the Standard Model. There should be three types of left-handed neutrinos. The right-handed neutrino becomes sterile. Spinors and gauge bosons derive their masses through coupling to the tachyons present in the spectrum via SSB and strings become point-particles below the critical temperature.
We consider central extensions of two dimensional abelian current algebra and Virasoro algebra and see that the sign of the Schwinger term changes if we arrange the Fourier modes of the fermion in the commutator in the order opposite to the normal. We argue that this is permissible in the case of fermions, but not in the case of bosons.
Redefining the vacuum state of a free twofold N=1 covariant supersymmetric string action as the one with all the world sheet fermionic excited states occupied, makes the theory anomaly free in D=4 with Minkowski signature. The theory thus describes a critical string in 3+1 dimensions as opposed to earlier N=2 supersymmetric theories describing a 2+2 dimensional target space. While in the NS sector the spectrum basically resembles the same for the standard N=1 superstring theory with one of the $N$ species in the background, in the R sector both the species of fermions and superconformal ghosts are required to describe the relevant spin operators to describe the fermion spectra. A crucial difference from D=10 case is that the fermion states are Dirac particles instead of Majorana-Weyl. Even though the full spectrum of the theory contains both bosons and fermions of various spin, there is no space-time supersymmetry due to obvious lack of triality.