Recursion relations from space-time supersymmetry

Basu, Anirban; Sethi, Savdeep

doi:10.1088/1126-6708/2008/09/081

Cited by 33 publications

(113 citation statements)

References 44 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…Next, we use the fact that upon acting on functions depending only on the GL(2)/U (1) factor parametrised by U = U 1 + iU 2 ∈ H 1 and y d , the Laplacian on E d+1 reduces to to [1, (4.65)] 11 The normalisation of the character is defined such that the action of the Cartan torus element on the lowest weight representation Λ k is normalised to y k . In other words, we write the torus element as exp(− i log(yi)hi), where the hi are the canonical Chevalley generators that need to be evaluated in the lowest weight representation.…”

Section: Laplace Identitiesmentioning

confidence: 99%

$1/8$-BPS couplings and exceptional automorphic functions

2020

View full text Add to dashboard Cite

Unlike the R 4 and ∇ 4 R 4 couplings, whose coefficients are Langlands-Eisenstein series of the U-duality group, the coefficient E (d) (0,1) of the ∇ 6 R 4 interaction in the low-energy effective action of type II strings compactified on a torus T d belongs to a more general class of automorphic functions, which satisfy Poisson rather than Laplace-type equations. In earlier work [1], it was proposed that the exact coefficient is given by a two-loop integral in exceptional field theory, with the full spectrum of mutually 1/2-BPS states running in the loops, up to the addition of a particular Langlands-Eisenstein series.Here we compute the weak coupling and large radius expansions of these automorphic functions for any d. We find perfect agreement with perturbative string theory up to genus three, along with non-perturbative corrections which have the expected form for 1/8-BPS instantons and bound states of 1/2-BPS instantons and anti-instantons. The additional Langlands-Eisenstein series arises from a subtle cancellation between the two-loop amplitude with 1/4-BPS states running in the loops, and the three-loop amplitude with mutually 1/2-BPS states in the loops. For d = 4, the result is shown to coincide with an alternative proposal [2] in terms of a covariantised genus-two string amplitude, due to interesting identities between the Kawazumi-Zhang invariant of genustwo curves and its tropical limit, and between double lattice sums for the particle and string multiplets, which may be of independent mathematical interest.

show abstract

Section: Laplace Identitiesmentioning

confidence: 99%

$1/8$-BPS couplings and exceptional automorphic functions

2020

View full text Add to dashboard Cite

show abstract

“…The general form of self-dual field strength is 11) and that of anti-self-dual field strength is 12) where h AB and h AB are symmetric tensors in A and B. Although H sf and H asf is not manifestly antisymmetric in the pairs of indices {A i }, {B i }, {C i }, one can show the explicitly antisymmetric property by the identities 13) and 14) where the notation of antisymmetrization in indicies is defined as where we have specified the SU(4) R-symmetry indices.…”

Section: Jhep09(2015)098mentioning

confidence: 99%

“…Furthermore, for N = 4 quantum mechanics, one can show that the coefficient of six-derivative terms are completely determined by that of four derivatives [5]. Supersymmetry has also been extensively used to study higher derivative terms in the effective actions of maximal supersymmetric gravity theories with many interesting exact results have been obtained [6][7][8][9][10][11][12].…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Exact coefficients for higher dimensional operators with sixteen supersymmetries

Chen

Huang

Wen

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) Rsymmetry, we demonstrate that the coefficients of abelian operators F n with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F 4 . As the F 4 coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N = 8 as well as six-dimensional N = (2, 0), (1, 0) and (1, 1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.

show abstract

“…This leads to Poisson equations on moduli space, where the source terms are given by couplings at lower orders in the α ′ expansion. These source terms that arise from the supervariation of the form δ (p) S (q) are at least quadratic in the couplings, where one factor arises from the coupling in S (q) while the other factor arises from the coupling in the corrected supersymmetry transformation δ (p) whose form is dictated by the closure of the supersymmetry algebra [7] 8 and involves an appropriate coupling in S (p) . For the D 6 R 4 interaction, this leads to the perturbative contributions [20]…”

Section: Supersymmetry and S-duality Constraints On Transcendentalitymentioning

confidence: 99%

Transcendentality violation in type IIB string amplitudes

Basu

2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We analyze transcendentality for certain terms that arise in multiloop amplitudes in the low momentum expansion of the four graviton amplitude in type IIB string theory in ten dimensions, based on the constraints of supersymmetry and S-duality.This leads to several contributions that violate transcendentality beyond one loop at all orders in the low momentum expansion. We also perform a similar analysis for the five graviton amplitude, obtaining contributions that involve single-valued multiple zeta values beyond tree level.

show abstract

Recursion relations from space-time supersymmetry

Cited by 33 publications

References 44 publications

$1/8$-BPS couplings and exceptional automorphic functions

$1/8$-BPS couplings and exceptional automorphic functions

Exact coefficients for higher dimensional operators with sixteen supersymmetries

Transcendentality violation in type IIB string amplitudes

Contact Info

Product

Resources

About