# The D6ℛ4 term from three loop maximal supergravity

@article{Basu2014TheDT, title={The D6ℛ4 term from three loop maximal supergravity}, author={Anirban Basu}, journal={Classical and Quantum Gravity}, year={2014}, volume={31} }

We consider the D 6 R 4 ?> term which is the leading contribution in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity. We calculate the moduli dependent coefficient of this term in eleven dimensional supergravity compactified on T2. Only diagrams that involve the Mercedes skeleton contribute resulting in a compact expression involving an integral over six Schwinger parameters. We express this integral as an integral over the moduli of an auxiliary T3…

## 23 Citations

### Cancellation of divergences up to three loops in exceptional field theory

- Geology
- 2017

A bstractWe consider the tetrahedral three-loop diagram in Ed exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes…

### Non-BPS interactions from the type II one loop four graviton amplitude

- Mathematics, Physics
- 2016

We obtain T-duality invariant second order differential equations satisfied by the D 8 4 and D 10 4 interactions from the low energy expansion of the one loop four graviton amplitude in…

### Loops in exceptional field theory

- Geology
- 2015

A bstractWe study certain four-graviton amplitudes in exceptional field theory in dimensions D ≥ 4 up to two loops. As the formulation is manifestly invariant under the U-duality group E11−Dℤ$$…

### Perturbative type II amplitudes for BPS interactions

- Mathematics
- 2016

We consider the perturbative contributions to the 4 ?> , D 4 4 ?> and D 6 4 ?> interactions in toroidally compactified type II string theory. These BPS interactions do not receive perturbative…

### Constraining non-BPS interactions from counterterms in three loop maximal supergravity

- Physics
- 2015

The structure of one, two and three loop counterterms imposes strong constraints on several non-BPS interactions in the low momentum expansion of the three loop, four graviton amplitude in maximal…

### Non-analytic terms from nested divergences in maximal supergravity

- Mathematics
- 2016

The D 4 4 and D 6 4 coefficient functions in the effective action of type II string theory compactified on Td contain terms of the form 1 ln g d and 2 ( ln g d ) 2 in specific dimensions,…

### Low momentum expansion of one loop amplitudes in heterotic string theory

- Physics
- 2017

A bstractWe consider the low momentum expansion of the four graviton and the two graviton-two gluon amplitudes in heterotic string theory at one loop in ten dimensions, and analyze contributions upto…

### Poisson equation for the Mercedes diagram in string theory at genus one

- Mathematics, Physics
- 2016

The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three-loop Feynman diagram contributes to the D 12 4 ?>…

### The two ∇6R4 type invariants and their higher order generalisation

- Mathematics
- 2015

A bstractWe show that there are two distinct classes of ∇6R4 type supersymmetry invariants in maximal supergravity. The second class includes a coupling in F2∇4R4 that generalises to 1/8 BPS…

### D6R4 curvature corrections, modular graph functions and Poincaré series

- Mathematics
- 2018

A bstractIn this note we study the U-duality invariant coefficient functions of higher curvature corrections to the four-graviton scattering amplitude in type IIB string theory compactified on a…

## References

SHOWING 1-10 OF 54 REFERENCES

### Two loops in eleven-dimensions

- Physics
- 2000

The two-loop Feynman diagram contribution to the four-graviton amplitude of eleven-dimensional supergravity compactified on a two-torus, T^2, is analyzed in detail. The Schwinger parameter…

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

- Physics
- 2008

The low-momentum expansion of the two-loop four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a circle and a two-torus is considered up to terms of order S6 4…

### Matching the D6ℛ4 interaction at two-loops

- Mathematics, Physics
- 2014

A bstractThe 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…

### Duality and higher derivative terms in M theory

- Physics
- 2006

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D6 4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions…

### The low energy expansion of the one-loop type II superstring amplitude

- Physics
- 2000

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a…

### Three-Loop Superfiniteness of N=8 Supergravity

- Physics
- 2007

We construct the three-loop four-point amplitude of N = 8 supergravity using the unitarity method. The amplitude is ultraviolet ﬁnite in four dimensions. Novel cancellations, not predicted by…

### Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N = 8 Supergravity

- Physics
- 2008

Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of $\mathcal{N}=8$ supergravity in which all ultraviolet cancellations are made manifest. The…

### Cancellations beyond finiteness in N=8 supergravity at three loops.

- PhysicsPhysical review letters
- 2007

Novel cancellations not predicted by traditional superspace power-counting arguments render its degree of divergence in D dimensions no worse than that of N=4 super-Yang-Mills theory--a finite theory in four dimensions.