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

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

The implementation and evaluation of an undergraduate virtual reality surveying application

Multi-media applications are increasingly being used to enhance the delivery of on-site and distance learning teaching material. However, production costs are often prohibitive, both in terms of capital investment and development time. Hence it is surprising that authors comment on the failure to adequately evaluate new educational software applications. This paper evaluates an interactive multi-media levelling resource, which comprises text-based guides, video instruction, photo-realistic panoramic scenes and multi-row object movies. Students explore 360 degree images of building sites, using traditional computer input devices, and click on hot spots to gather detailed information about the position of the optical level and staff. Readings are taken directly from the staff and students record backsights and foresights as various change points are introduced. On completion of the levelling exercise, 192 first year undergraduate students completed an evaluation based upon a series of statements drawn from technology-based training literature. The findings suggest that the exercise complements traditional learning approaches, maintains student interest, and reinforces understanding. However, significant differences in student ratings for part-time and full-time cohorts emphasise the importance of designing resources that accommodate the needs of varying student profiles. Suggestions for enhanced interactivity are offered and new areas for development allied to construction technology are identified

Infrared divergences and harmonic anomalies in the two-loop superstring effective action

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are creditedArticle funded by SCOAP3. This research is partially supported by STFC (Grant ST/L000415/1, String theory, gauge theory & duality

Constraints on Automorphic Forms of Higher Derivative Terms from Compactification

By dimensionally reducing the higher derivative corrections of ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1} automorphic forms that occur in d=10-n dimensions. In particular we argue that these automorphic forms involve the representation of E_{n+1} with fundamental weight \lambda^{n+1}, which is also the representation to which the string charges in d dimensions belong. We also consider a similar calculation for the reduction of higher derivative terms in eleven-dimensional M-theory.Comment: Minor corrections, to appear in JHE

BPS Saturated Amplitudes and Non-perturbative String Theory

The study of the special F^4 and R^4 in the effective action for the Spin(32)/Z_2 and type II strings shed some light on D-brane calculus and on instanton contributions counting. The D-instanton case is discussed separately

Higher derivative type II string effective actions, automorphic forms and E11

By dimensionally reducing the ten-dimensional higher derivative type IIA string theory effective action we place constraints on the automorphic forms that appear in the effective action in lower dimensions. We propose a number of properties of such automorphic forms and consider the prospects that E11 can play a role in the formulation of the higher derivative string theory effective action.Comment: 34 page

Eisenstein series for infinite-dimensional U-duality groups

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published in JHE

M-Theory and Maximally Supersymmetric Gauge Theories

In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.Comment: Minor corrections and an added acknowledgement. Accepted for publication in Annual Review

Exploring transcendentality in superstring amplitudes

Abstract It is well known that the low energy expansion of tree-level superstring scattering amplitudes satisfies a suitably defined version of uniform transcendentality. In this paper it is argued that there is a natural extension of this definition that applies to the genus-one four-graviton Type II superstring amplitude to all orders in the low-energy expansion. To obtain this result, the integral over the genus-one moduli space is partitioned into a region $$\mathrm{\mathcal{M}}$$ ℳ R surrounding the cusp and its complement $$\mathrm{\mathcal{M}}$$ ℳ L , and an exact expression is obtained for the contribution to the amplitude from $$\mathrm{\mathcal{M}}$$ ℳ R . The low-energy expansion of the $$\mathrm{\mathcal{M}}$$ ℳ R contribution is proven to be free of irreducible multiple zeta-values to all orders. The contribution to the amplitude from $$\mathrm{\mathcal{M}}$$ ℳ L is computed in terms of modular graph functions up to order D 12 $$\mathrm{\mathcal{R}}$$ ℛ 4 in the low-energy expansion, and general arguments are used beyond this order to conjecture the transcendentality properties of the $$\mathrm{\mathcal{M}}$$ ℳ L contributions. Uniform transcendentality of the full amplitude holds provided we assign a non-zero weight to certain harmonic sum functions, an assumption which is familiar from transcendentality assignments in quantum field theory amplitudes.</jats:p