TY - JOUR

T1 - Spin structures in string theory

AU - Seiberg, N.

AU - Witten, E.

N1 - Funding Information:
The work of N. S. was supported in part by DOE contract DE-AC02-76ER02220 and that of E. W. by NSF grant PHYS0-19754. We would like to thank V. Kaplunovsky for assistance. After completion of this paper we became aware of other related work. Vafa \[11\] uses a technique similar to that of sect. 3 to determine the phases in theories based on orbifolds. Modular invariant combinations of partition functions somewhat similar to those in sect. 4, but more intricate, have been constructed by Dixon and Harvey \[12\], who found and studied in detail a tachyon free model, and by Alvarez-Gaum~ et al. \[13\].N arain \[14\]a lso studied similar theories.

PY - 1986/10/13

Y1 - 1986/10/13

N2 - The effect of modular transformations which change the spin structure of the string world-sheet is discussed. Invariance of string perturbation theory under such transformations forces us to sum over different spin structures with well defined coefficients. The sum over spin structures amounts to performing the GSO projections. We explain why the GSO projections is compatible with unitarit; that is, why wrong G-parity states are not produced in pairs. On the contrary, we show that unitarity requires either the GSO projection, which gives a supersymmetric spectrum, or another projection which removes the massless spin- 3 2 particle from the spectrum. This is in agreement with the familiar idea that a consistent theory with a massless spin- 3 2 particle must be supersymmetric. These considerations lead us to find four new string theories in ten dimensions. Although they all have tachyons, they are otherwise consistent, modular invariant and unitary. One of these theories is particularly interesting since it has anomaly free chiral fermions in ten dimensions.

AB - The effect of modular transformations which change the spin structure of the string world-sheet is discussed. Invariance of string perturbation theory under such transformations forces us to sum over different spin structures with well defined coefficients. The sum over spin structures amounts to performing the GSO projections. We explain why the GSO projections is compatible with unitarit; that is, why wrong G-parity states are not produced in pairs. On the contrary, we show that unitarity requires either the GSO projection, which gives a supersymmetric spectrum, or another projection which removes the massless spin- 3 2 particle from the spectrum. This is in agreement with the familiar idea that a consistent theory with a massless spin- 3 2 particle must be supersymmetric. These considerations lead us to find four new string theories in ten dimensions. Although they all have tachyons, they are otherwise consistent, modular invariant and unitary. One of these theories is particularly interesting since it has anomaly free chiral fermions in ten dimensions.

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U2 - 10.1016/0550-3213(86)90297-X

DO - 10.1016/0550-3213(86)90297-X

M3 - Article

AN - SCOPUS:33645917666

SN - 0550-3213

VL - 276

SP - 272

EP - 290

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 2

ER -