Theoretical Physicshttps://qmro.qmul.ac.uk/xmlui/handle/123456789/35672019-04-22T14:34:05Z2019-04-22T14:34:05ZHigher Genus Modular Graph Functions, String Invariants, and their Exact AsymptoticsD Hoker, EGreen, MBPioline, Bhttps://qmro.qmul.ac.uk/xmlui/handle/123456789/569082019-04-18T09:34:12Z2018-10-10T00:00:00ZHigher Genus Modular Graph Functions, String Invariants, and their Exact Asymptotics
D Hoker, E; Green, MB; Pioline, B
The concept and the construction of modular graph functions are generalized from genus-one to higher genus surfaces. The integrand of the four-graviton superstring amplitude at genus-two provides a generating function for a special class of such functions. A general method is developed for analyzing the behavior of modular graph functions under non-separating degenerations in terms of a natural real parameter t. For arbitrary genus, the Arakelov–Green function and the Kawazumi–Zhang invariant degenerate to a Laurent polynomial in t of degree (1, 1) in the limit t→ ∞. For genus two, each coefficient of the low energy expansion of the string amplitude degenerates to a Laurent polynomial of degree (w, w) in t, where w + 2 is the degree of homogeneity in the kinematic invariants. These results are exact to all orders in t, up to exponentially suppressed corrections. The non-separating degeneration of a general class of modular graph functions at arbitrary genus is sketched and similarly results in a Laurent polynomial in t of bounded degree. The coefficients in the Laurent polynomial are generalized modular graph functions for a punctured Riemann surface of lower genus.
2018-10-10T00:00:00ZType D spacetimes and the Weyl double copyLuna, AMONTEIRO, RJFNicholson, IO'Connell, Dhttps://qmro.qmul.ac.uk/xmlui/handle/123456789/567902019-04-12T12:22:58Z2019-02-18T00:00:00ZType D spacetimes and the Weyl double copy
Luna, A; MONTEIRO, RJF; Nicholson, I; O'Connell, D
We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type—the Weyl double copy—relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr–Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Liénard–Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi–Hanson instanton.
2019-02-18T00:00:00ZDual conformal invariance for form factorsBianchi, LBrandhuber, APanerai, RTravaglini, Ghttps://qmro.qmul.ac.uk/xmlui/handle/123456789/563772019-03-21T10:33:38Z2019-02-20T00:00:00ZDual conformal invariance for form factors
Bianchi, L; Brandhuber, A; Panerai, R; Travaglini, G
Form factors of the stress-tensor multiplet operator in N=4 supersymmetric Yang-Mills reveal surprisingly simple structures similar to those appearing in scattering amplitudes. In this paper we show that, as for the case of amplitudes, they also enjoy dual conformal symmetry. We compute the dual conformal anomaly at one loop for an arbitrary number of particles and generic helicities, which matches the expression of the dual conformal anomaly of amplitudes, and perform explicit checks for MHV and NMHV one-loop form factors. In the NMHV case the realisation of dual conformal symmetry requires a delicate cancellation of offending terms arising from three-mass triangles, which we explicitly check in the case of the four-point NMHV form factor.
2019-02-20T00:00:00ZForm factor recursion relations at loop levelBianchi, LBrandhuber, APanerai, RTravaglini, Ghttps://qmro.qmul.ac.uk/xmlui/handle/123456789/563752019-03-21T10:33:41Z2019-02-27T00:00:00ZForm factor recursion relations at loop level
Bianchi, L; Brandhuber, A; Panerai, R; Travaglini, G
We introduce a prescription to define form factor integrands at loop level in planar N=4 supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete one-loop examples to illustrate and validate our prescription for form factor integrands.
2019-02-27T00:00:00Z