Two-loop superstrings on orbifold compactifications

Abstract

The two-loop chiral measure for superstring theories compactified on Z 2 reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure in the twisted sectors and the identification of a subtle worldsheet supersymmetric and supermoduli dependent shift in the Prym period. The construction is generalized to compactifications which involve more general NS backgrounds preserving worldsheet supersymmetry. The measures are unambiguous and independent of the gauge slice.Two applications are presented, both to superstring compactifications where 4 dimensions are Z 2 -twisted and where the GSO projection involves a chiral summation over spin structures. The first is an orbifold by a single Z 2 -twist; here, orbifolding reproduces a supersymmetric theory and it is shown that its cosmological constant indeed vanishes. The second model is of the type proposed by Kachru-KumarSilverstein and additionally imposes a Z 2 -twist by the parity of worldsheet fermion number; it is shown here that the corresponding cosmological constant does not vanish pointwise on moduli space.

Asyzygies, modular forms, and the superstring measure II

“…This form of Riemann identities is closely related to Riemann identities on Prym varieties, which appeared in the study of the cosmological constant in certain orbifold models with broken supersymmetry [8,11].…”

“…Any of the 15 twists may be expressed (see for example [8]) as the sum of two odd spin structures, ε = ν a + ν b for a = b, all such spin structures may be parametrized by…”

Non-supersymmetric D-branes with vanishing cylinder amplitudes in asymmetric orbifolds

“…For instance, for the B-type gluing condition, we obtain R . 9 Obviously the relation (3.43) yields the self-overlap that depends on the parameter θ r , as opposed to the first and second cases. The resultant amplitude does not vanish generically.…”

“…The attempts of the construction of non-SUSY vacua with vanishing cosmological constant have been initiated by [1][2][3] based on some non-abelian orbifolds, followed by closely related studies e.g. in [4][5][6][7][8][9]. More recently, several non-SUSY vacua with this property have been constructed as asymmetric orbifolds [10] by simpler cyclic groups in [11,12].…”

Two-loop string theory on null compactifications

“…This process terminates precisely when k is equal to the index (A.23), and then C k = C (µ) is the desired Schreier transversal for Γ (µ) . For example, when µ = 2 the subgroup Γ (2) has index 6 and C (2) = {1 1 2 , S, S T, S T 2 , S T 3 , S T 2 S} is a Schreier transversal for Γ (2) . The corresponding elliptic fundamental domain (A.14) is depicted in Figure 1.…”