N=8 Counterterms and E7(7) Current Conservation

We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the presence of N=8 supergravity counterterms using the momentum space helicity formalism, which significantly simplifies the calculations. The main result is that the 4-point counterterms at any loop order L are forbidden by the E7(7) current conservation identity. We also clarify the relation between linearized and full non-linear superinvariants as candidate counterterms. This enables us to show that all n-point counterterms at L=7, 8 are forbidden since they provide a non-linear completions of the 4-point ones. This supports and exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness of N=8 supergravity.Comment: 18 page

Heterotic Action in SUGRA-SYM Background

We consider the generalization of the heterotic action considered by Cherkis and Schwarz where the chiral bosons are introduced in a manifestly covariant way using an auxiliary field. In particular, we construct the kappa-symmetric heterotic action in ten-dimensional supergravity background coupled to super Yang-Mills theory and prove its kappa-symmetry. The usual Bianchi identity of Type I supergravity with super Yang-Mills dH_3= -\tr F\wedge F is crucially used. For technical reason, the Yang-Mills field is restricted to be abelian.Comment: 12 pages, no figures, added comments in the acknowledgmen

Counterterms vs. Dualities

We investigate and clarify the mutual compatibility of the higher order corrections arising in supergravity and string theory effective actions and the non-linear duality symmetries of these theories. Starting from a conventional tree level action leading to duality invariant equations of motion, we show how to accommodate duality invariant counterterms given as functionals of both electric and magnetic fields in a perturbative expansion, and to deduce from them a non-polynomial bona fide action satisfying the Gaillard-Zumino constraint. There exists a corresponding consistency constraint in the non-covariant Henneaux-Teitelboim formalism which ensures that one can always restore diffeomorphism invariance by perturbatively solving this functional identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F and F^4 counterterms in Maxwell theory.Comment: 15 page

Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.Comment: 25 pages, typos corrected, references adde

R^4 counterterm and E7(7) symmetry in maximal supergravity

The coefficient of a potential R^4 counterterm in N=8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R^4 term respects N=8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R^4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R^4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio

Stringy KLT relations, global symmetries, and E_7(7) violation

We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.Comment: 23 pages, published versio

A simple approach to counterterms in N=8 supergravity

We present a simple systematic method to study candidate counterterms in N=8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D^{2k} R^n +... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n>4, we find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D^{2k}R^n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D^4 R^6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/allowed candidate counterterms is summarized in a colorful chart.Comment: 25 pages, 1 figure, published versio

The D^{2k} R^4 Invariants of N=8 Supergravity

The existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R^4 was established long ago by on-shell superspace arguments. Superspace and string theory methods have also established analogous higher dimensional D^{2k} R^4 invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R^4 invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D^{2k} R^4 operators.Comment: 17 page

Solution to the Ward Identities for Superamplitudes

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and R-invariant form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n-4) corresponding to the rectangular Young diagram with N columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in N=4 gauge theory. We also analyze the more significant reduction that occurs in N=8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.Comment: 29 pages, published versio

On the infrared behaviour of 3d Chern-Simons theories in N=2 superspace

We discuss the problem of infrared divergences in the N=2 superspace approach to classically marginal three-dimensional Chern-Simons-matter theories. Considering the specific case of ABJM theory, we describe the origin of such divergences and offer a prescription to eliminate them by introducing non-trivial gauge-fixing terms in the action. We also comment on the extension of our procedure to higher loop order and to general three-dimensional Chern-Simons-matter models.Comment: 26 pages, 6 figures, JHEP3; v2: minor corrections and references added; v3: introduction expanded, presentation of section 3.3.1 improved, references added, version to appear in JHE