NSR superstring measures revisited

Morozov, A.

doi:10.1088/1126-6708/2008/05/086

Cited by 24 publications

(21 citation statements)

References 125 publications

(193 reference statements)

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“…vanishes identically on T g in any genus (physically f 4 is interpreted as the appropriate measure for the E 8 theory, f 2 4 -for E 8 × E 8 , and f 8 -for SO (32)). For g ≤ 3 the identical vanishing of this modular form on T g = H g is a consequence of Riemann's bilinear addition theorem.…”

Section: Lemma 7 ([28]) We Havementioning

confidence: 99%

See 1 more Smart Citation

The superstring cosmological constant and the Schottky form in genus 5

Grushevsky¹,

Manni²

2011

ajm

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Abstract. Combining certain identities for modular forms due to Igusa with Schottky-Jung relations, we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5. The vanishing of this cosmological constant turns out to be equivalent to the long-conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves M 5 , and we disprove this conjecture, thus showing that the cosmological constant for the proposed ansatz does not vanish identically. We exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant. We also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized Schottky-Jung identities hold.

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Section: Lemma 7 ([28]) We Havementioning

confidence: 99%

“…In [37] the second-named author proved that in genus 5 these holomorphic square roots are indeed well-defined modular forms on a suitable covering of M 5 , and thus that an ansatz is well-defined for g = 5. For a review and further developments, see Morozov [32,33]. See also [30] for a different approach.…”

Section: Introductionmentioning

confidence: 99%

The superstring cosmological constant and the Schottky form in genus 5

Grushevsky¹,

Manni²

2011

ajm

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“…Dalla Piazza and van Geemen in [4] proved the uniqueness of the modular form in genus 3 satisfying the factorization constraints. Morozov in [22] surveyed this work and gave an alternative proof that factorization constraints are satisfied for the ansatz; in [23] he has also investigated the 1,2,3-point functions of the proposed ansatz, proving under certain nontrivial mathematical assumption that they vanish on the hyperelliptic locus.…”

Section: Introductionmentioning

confidence: 99%

The Vanishing of Two-Point Functions for Three-Loop Superstring Scattering Amplitudes

Grushevsky

Manni

2009

Commun. Math. Phys.

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Abstract. In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen [2] vanishes. Our proof uses the reformulation of ansatz given in [8], theta functions, and specifically the theory of the Γ 00 linear system on Jacobians introduced by van Geemen and van der Geer [6]. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong [11,12,13,14,17,18], we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera [8,24,3].

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“…As of this writing it remains an open question whether the corresponding conditions can be satisfied by a Teichmuller modular form beyond g = 5. See [16] for an entry to the physics literature. In Table 1, we give some Fourier coefficients for a (T ; Ξ 2 [0]) using the above polynomial in the thetanullwerte (1).…”

Section: An Applicationmentioning

confidence: 99%

The Chiral Superstring Siegel Form in Degree Two Is a Lift

Poor

Yuen

2012

Journal of the Korean Mathematical Society

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Abstract. We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group Γ 1 (1, 2) to Siegel modular cusp forms over certain subgroups Γ para (t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

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NSR superstring measures revisited

Abstract: We review the remarkable progress in evaluating the NSR superstring measures, originated by E.D'Hoker and D.Phong. These recent results are presented in the old-fashioned form, which allows us to highlight the options that have been overlooked in original considerations in late 1980's.

Cited by 24 publications

References 125 publications

The superstring cosmological constant and the Schottky form in genus 5

The superstring cosmological constant and the Schottky form in genus 5

The Vanishing of Two-Point Functions for Three-Loop Superstring Scattering Amplitudes

The Chiral Superstring Siegel Form in Degree Two Is a Lift

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