Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

Berkovits, Nathan

doi:10.1088/1126-6708/2004/09/047

Cited by 205 publications

(589 citation statements)

References 74 publications

(108 reference statements)

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“…Most of the analysis involves the first few terms in the α ′ expansion of the effective action; for a selection of papers, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Of particular interest to us are interactions in ten-dimensional type IIB Here E s (τ,τ ) is the non-holomorphic Eisenstein series given in Appendix B.…”

Section: Introductionmentioning

confidence: 99%

Recursion relations from space-time supersymmetry

Basu

Sethi

2008

J. High Energy Phys.

111

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We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling dependence of theĜ 2k λ 16 interaction in type IIB string theory. Using supersymmetry, we show that each of these interactions satisfies a Poisson equation on the moduli space with sources determined by lower momentum interactions. We argue that these protected couplings are only renormalized by a finite number of string loops together with nonperturbative terms. Finally, we explore some consequences of the Poisson equationfor low values of k.

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Section: Introductionmentioning

confidence: 99%

Recursion relations from space-time supersymmetry

Basu

Sethi

2008

J. High Energy Phys.

111

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“…Since the worldsheet action is quadratic, it is straightforward to compute manifestly super-Poincaré covariant N -point tree amplitudes using this formalism and, last year, it was shown how to compute multiloop amplitudes [4]. In addition to proving various vanishing theorems related to perturbative finiteness and S-duality [4], super-Poincaré covariant massless fourpoint one-loop [4] and two-loop [5] amplitudes were explicitly computed.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and Ramond-Neveu-Schwarz Formalisms

Berkovits¹,

2006

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“…Using the minimal version of the pure spinor formalism which involves a bosonic ghost satisfying the pure spinor constraint m 0, a multiloop prescription was defined in [8] and used to prove certain vanishing theorems. One theorem stated that massless N-point multiloop amplitudes are vanishing when N 3, which is related to perturbative finiteness of the super string [9].…”

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confidence: 99%

New Higher-DerivativeR4Theorems for Graviton Scattering

Berkovits

2007

Phys. Rev. Lett.

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The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R 4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, @ n R 4 terms in the Type II effective action do not receive perturbative contributions above n=2 loops. The second theorem states that when n 8, perturbative contributions to @ n R 4 terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d 4 N 8 supergravity is ultraviolet finite up to eight loops. DOI: 10.1103/PhysRevLett.98.211601 PACS numbers: 11.25.Db Introduction.-The main success of superstring theory is that it provides a consistent quantum theory of gravity which replaces general relativity at small distances. It is therefore important to know how graviton scattering at high energies differs in superstring theory from general relativity. For scattering amplitudes involving two incoming and two outgoing gravitons, the lowest-order deviation from general relativity comes from R 4 terms in the superstring effective action [1], and higher-order deviations come from @ n R 4 terms where @ n denotes n spacetime derivatives, R denotes the Riemann tensor, and Lorentz indices are suppressed. The structure of these @ n R 4 terms is believed to be tightly constrained by duality symmetries of the superstring [2]; however, these duality symmetries are difficult to prove since they involve nonperturbative effects. It is therefore important to compute @ n R 4 terms in perturbative superstring theory, both for studying deviations from general relativity and for testing the nonperturbative duality symmetries.A further motivation for studying the structure of @ n R 4 terms in Type II superstring theory is that they provide information about the maximally supersymmetric version of gravity in four dimensions which is called d 4 N 8 supergravity. In the early days of supersymmetry, d 4 N 8 supergravity was conjectured to be a consistent finite theory of gravity. It was later realized that d 4 N 8 supergravity probably has ultraviolet divergences which are eliminated only after including the massive states of superstring theory. However, the existence of these ultraviolet divergences in d 4 N 8 supergravity has never been proven, and it was recently shown by explicit computation that they are absent up to three loops [3]. Furthermore, it was argued in [2,4,5] that finiteness properties of d 4 N 8 supergravity are related to nonrenormalization theorems of @ n R 4 terms. For example, using the results described here that @ n R 4 terms do not get contributions above n=2 loops when n < 12, it was deduced in [5] that d 4 N 8 supergravity is ultraviolet finite up to 8 loops.Although there are several prescriptions available for computing superstring amplitudes, the most efficient pre-

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Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

Cited by 205 publications

References 74 publications

Recursion relations from space-time supersymmetry

Recursion relations from space-time supersymmetry

Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and Ramond-Neveu-Schwarz Formalisms

New Higher-DerivativeR4Theorems for Graviton Scattering

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