An ambiguity in fermionic string perturbation theory

Atick, Joseph J.; Rabin, Jeffrey M.; Sen, Ashoke

doi:10.1016/0550-3213(88)90285-4

Cited by 73 publications

(54 citation statements)

References 26 publications

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“…It had been conjectured to hold long ago, in part thanks to space-time supersymmetry [24]. Prior to the present derivation from first principles, many arguments in favor of this conjecture had been proposed in the literature [12,14,16,17,18,25].…”

Section: Non-renormalization Theoremsmentioning

confidence: 99%

“…In the earlier literature dating from the 1980's on multi-loops [7,8,9,10], (more extensive bibliographies were given in [2,11]) and specifically 2-loop [12,13,14,15] amplitudes, the gauge-fixing procedure was known to suffer from ambiguities, that is, the gauge-fixed amplitudes ended up being gauge slice dependent [9,16]. In retrospect, we know now that an ill-defined projection from supergeometries to their standard period matrices was implicitly used.…”

Section: Introductionmentioning

confidence: 99%

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Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

2005

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The N-point amplitudes for the Type II and Heterotic superstrings at two-loop order and for N ≤ 4 massless NS bosons are evaluated explicitly from first principles, using the method of projection onto super period matrices introduced and developed in the first five papers of this series. The gauge-dependent corrections to the vertex operators, identified in paper V, are carefully taken into account, and the crucial counterterms which are Dolbeault exact in one insertion point and de Rham closed in the remaining points are constructed explicitly. This procedure maintains gauge slice independence at every stage of the evaluation. Analysis of the resulting amplitudes demonstrates, from first principles, that for N ≤ 3, no two-loop corrections occur, while for N = 4, no two-loop corrections to the low energy effective action occur for R 4 terms in the Type II superstrings, and for F 4 , F 2 F 2 , F 2 R 2 , and R 4 terms in the Heterotic strings.

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Section: Non-renormalization Theoremsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

2005

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“…In both approaches, special choices for the worldsheet gravitini insertion points were made, the first in unitary gauge, the second following [15]. By now, however, the picture changing operator and BRST formalism is well-known to be gauge slice dependent [13], (see also [16,17,18,19]) a fact that casts doubts over the conclusions of both [9] and [14].…”

Section: Introductionmentioning

confidence: 99%

Two-loop superstrings on orbifold compactifications

2004

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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.

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“…In conclusion, we observe that the preceding mechanism for enforcing the GSO projection and producing a vanishing cosmological constant provides yet another distinction with the many earlier efforts to treat supermoduli [15,16,17,18,19,20,21,22] and resolve ambiguities [23,24,25] in superstring multiloop amplitudes. In particular, the earlier proposals based on the picture-changing operator Ansatz [15] inserted at various special points had all relied only on Riemann identities to insure both modular invariance and the vanishing of the cosmological constant [26,27,28].…”

Section: Vanishing Of the Cosmological Constantmentioning

confidence: 96%

Two-loop superstrings IV

D’Hoker¹,

Phong²

2002

Nuclear Physics B

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The slice-independent gauge-fixed superstring chiral measure in genus 2 derived in the earlier papers of this series for each spin structure is evaluated explicitly in terms of theta-constants. The slice-independence allows an arbitrary choice of superghost insertion points q 1 , q 2 in the explicit evaluation, and the most effective one turns out to be the split gauge defined by S δ (q 1 , q 2 ) = 0. This results in expressions involving bilinear theta-constants M. The final formula in terms of only thetaconstants follows from new identities between M and theta-constants which may be interesting in their own right. The action of the modular group Sp(4,Z) is worked out explicitly for the contribution of each spin structure to the superstring chiral measure. It is found that there is a unique choice of relative phases which insures the modular invariance of the full chiral superstring measure, and hence a unique way of implementing the GSO projection for even spin structure. The resulting cosmological constant vanishes, not by a Riemann identity, but rather by the genus 2 identity expressing any modular form of weight 8 as the square of a modular form of weight 4. The degeneration limits for the contribution of each spin structure are determined, and the divergences, before the GSO projection, are found to be the ones expected on physical grounds.

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An ambiguity in fermionic string perturbation theory

Cited by 73 publications

References 26 publications

Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

Two-loop superstrings on orbifold compactifications

Two-loop superstrings IV

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