Eluding SUSY at every genus on stable closed string vacua

Cacciatori, Sergio L.; Cardella, Matteo A.

doi:10.1007/jhep05(2011)124

Cited by 3 publications

(3 citation statements)

References 32 publications

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“…Using this method it was shown that non-tachyonic string configurations are characterised by a spectrum of physical excitations that not only must enjoy asymptotic supersymmetry but actually, at very large mass, bosonic and fermionic states are bound to follow a universal oscillating pattern, whose frequencies are related to the non-trivial zeroes of the Riemann ζfunction. Similar studies have then been generalised to higher genus [22][23][24] where similar constraints on the interactions of physical states are expected to emerge.…”

Section: Introductionmentioning

confidence: 73%

A new look at one-loop integrals in string theory

Angelantonj

Florakis

Pioline

2012

Communications in Number Theory and Physics

123

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We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional 'orbit method', keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to cases where the integrand function grows at most polynomially in the IR. Furthermore, we introduce new techniques in the case where 'unphysical tachyons' contribute to the one-loop couplings. These methods can be viewed as a modular invariant version of dimensional regularisation. As an example, we treat one-loop BPS-saturated couplings involving the d-dimensional Narain lattice and the invariant Klein j-function, and relate them to (shifted) constrained Epstein Zeta series of O(d, d; Z). In particular, we recover the well-known results for d = 2 in a few easy steps.

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Section: Introductionmentioning

confidence: 73%

A new look at one-loop integrals in string theory

Angelantonj

Florakis

Pioline

2012

Communications in Number Theory and Physics

123

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“…Other attempts to use the Rankin-Selberg method to compute string amplitudes or probe the asymptotic density of string states include[14][15][16][17][18][19].…”

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confidence: 99%

On the Rankin–Selberg method for higher genus string amplitudes

Florakis

Pioline

2017

Communications in Number Theory and Physics

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Closed string amplitudes at genus h ≤ 3 are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane. When the integrand is of rapid decay near the cusps, the integral can be computed by the Rankin-Selberg method, which consists of inserting an Eisenstein series E h (s) in the integrand, computing the integral by the orbit method, and finally extracting the residue at a suitable value of s. String amplitudes, however, typically involve integrands with polynomial or even exponential growth at the cusps, and a renormalization scheme is required to treat infrared divergences. Generalizing Zagier's extension of the Rankin-Selberg method at genus one, we develop the Rankin-Selberg method for Siegel modular functions of degree 2 and 3 with polynomial growth near the cusps. In particular, we show that the renormalized modular integral of the Siegel-Narain partition function of an even self-dual lattice of signature (d, d) is proportional to a residue of the Langlands-Eisenstein series attached to the h-th antisymmetric tensor representation of the T-duality group O(d, d, Z).

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“…The idea of applying Rankin-Selberg-type methods to compute one-loop modular integrals, albeit in a rather different way from[18], was first put forward in[19]. Steps towards extending them to higher genus were taken in[20].…”

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confidence: 99%

Rankin-Selberg methods for closed string amplitudes

Pioline¹

2014

Proceedings of Symposia in Pure Mathematics

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After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus h ≤ 3 are reduced to an integral of a Siegel modular function of degree h on a fundamental domain of the Siegel upper half plane. A direct computation is in general unwieldy, but becomes feasible if the integrand can be expressed as a sum over images under a suitable subgroup of the Siegel modular group: if so, the integration domain can be extended to a simpler domain at the expense of keeping a single term in each orbit -a technique known as the Rankin-Selberg method. Motivated by applications to BPS-saturated amplitudes, Angelantonj, Florakis and I have applied this technique to one-loop modular integrals where the integrand is the product of a Siegel-Narain theta function times a weakly, almost holomorphic modular form. I survey our main results, and take some steps in extending this method to genus greater than one.

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Eluding SUSY at every genus on stable closed string vacua

Cited by 3 publications

References 32 publications

A new look at one-loop integrals in string theory

A new look at one-loop integrals in string theory

On the Rankin–Selberg method for higher genus string amplitudes

Rankin-Selberg methods for closed string amplitudes

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