The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy
expansion of the two-loop four-graviton amplitude in type II superstring theory
is known to be proportional to the integral of the Zhang-Kawazumi (ZK)
invariant over the moduli space of genus-two Riemann surfaces. We demonstrate
that the ZK invariant is an eigenfunction with eigenvalue 5 of the
Laplace-Beltrami operator in the interior of moduli space. Exploiting this
result, we evaluate the integral of the ZK invariant explicitly, finding
agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted
on the basis of S-duality and supersymmetry. A review of the current
understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring
theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is
included.Comment: 40 pages, various typos and coefficients corrected in version 

D'Hoker, E

Green, MB

Pioline, B

Russo, R

Journal of High Energy Physics

English

arXiv

Eric D’Hoker

Michael B. Green

Boris Pioline

Rodolfo Russo

Springer - Publisher Connector

Matching the D 6ℛ4 interaction at two-loops

Queen Mary Research Online

Matching the (DR4)-R-6 interaction at two-loops

A new look at one-loop integrals in string theory,

A Note on nonperturbative R4 couplings,

Asymptotic behavior of the Kawazumi-Zhang invariant for degenerating Riemann surfaces,

Automorphic properties of low energy string amplitudes in various dimensions,

Chiral Bosonization, Determinants and the String Partition Function,

Die Differentialgleichungen in der Theorie der

Duality and higher derivative terms in M-theory,

Eisenstein series and string thresholds,

Eisenstein series for higher-rank groups and string theory amplitudes,

Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms,

Explizite Bestimmung der Randflhen des Fundamentalbereiches der Modulgruppe zweiten Grades,

Gauge slice independence of the N-point function,

Gross-Schoen Cycles and Dualising Sheaves,

Introductory Lectures to Siegel Modular Forms,

Johnson’s homomorphisms and the Arakelov Green function,

Lectures on two loop superstrings,

Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory,

Manifest Ultraviolet Behavior for the Three-Loop Four-Point

Modular properties of two-loop maximal supergravity and connections with string theory,

Notes On Holomorphic String And Superstring Theory Measures Of Low Genus,

On R4 threshold corrections in IIB string theory and (p, q) string instantons,

One loop in eleven-dimensions,

R4 couplings and automorphic unipotent representations,

Rankin-Selberg methods for closed string amplitudes,

Scalar field theory limits of bosonic string amplitudes,

Second variation of Zhang’s λ-invariant on the moduli space of curves,

String theory dualities and supergravity divergences,

Supersymmetry constraints on type IIB supergravity,

Symplectic Geometry,

The Asymptotics of the Arakelov-Green’s Function and Faltings’

The closed-string 3-loop amplitude and S-duality,

The D4R4 term in type IIB string theory on

The D6R4 term in type IIB string theory on

The Gˆ4λ16 term in IIB supergravity,

The Geometry of String Perturbation Theory,

The Low-energy expansion of the one loop type-II superstring amplitude,

The Rankin-Selberg method for automorphic functions which are not of rapid decay,

Topics in Two-Loop Superstring Perturbation Theory,

Tropical Amplitudes,

Two loop superstrings.

Two loop superstrings. II. The Chiral measure on moduli space,

Two loop superstrings. IV: the Cosmological constant and modular forms,

Two loops in eleven-dimensions,

Two-loop superstrings and S-duality,

Two-loop superstrings VI: non-renormalization theorems and the 4-point function,

Unity of superstring dualities,

Zhang-Kawazumi Invariants and Superstring Amplitudes,

The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included.The coefficient of the D$^{6}$ℛ$^{4}$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop D$^{6}$ℛ$^{4}$ interaction predicted on the basis of S-duality and super-symmetry. A review of the current understanding of the D$^{2}^{p}$ ℛ$^{4}$ interactions in type II superstring theory compactified on a torus T$^{d}$ with p ≤ 3 and d ≤ 4 is included.The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included

D'Hoker, Eric

Green, Michael B.

Pioline, Boris

Russo, Rodolfo

CERN Document Server

Matching the $D^{6}R^{4}$ interaction at two-loops

Matching the 
              ℛ interaction at two-loops

40 pages, various typos and coefficients corrected in version 2International audienceThe coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included

D’Hoker, Eric

Archive Ouverte en Sciences de l'Information et de la Communication

The coefficient of the D6R4 interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop D6R4 interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the D2pR4 interactions with p ≤ 3 is included

Eric D&apos

CiteSeerX

Matching the D6R4 interaction at two-loops

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Matching the (DR4)-R-6 interaction at two-loops

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Queen Mary Research Online

CERN Document Server

Springer - Publisher Connector

Archive Ouverte en Sciences de l'Information et de la Communication

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