Scattering Amplitudes from Rational Maps and Correlators in AdS/CFT

Zhang, Shun-Qing

Scattering Amplitudes from Rational Maps and Correlators in AdS/CFT

Shun-Qing Zhang
(
- Queen Mary, U. of London (main)
)

2023

184 pages

Supervisor:

Congkao Wen
(
- Queen Mary, U. of London (main)
)

Thesis: PhD

Queen Mary, U. of London (main)

(2023)

Published: 2023

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Abstract: (Queen Mary, U. of London (main))

This thesis focuses on novel techniques of computing scattering amplitudes and correlation functions in quantum field theories. We begin with the twistor formulation of amplitudes in six dimensions (6D), which compute tree-level

n

-point scattering amplitudes in (2,0) M5-brane (as well as (1,1) D5-brane), (1,1) super Yang-Mills (SYM), (2,2) supergravity (SUGRA), and (2,0) SUGRA theories. We also obtain loop amplitudes in lower dimensions, 4D for instance, by performing dimensional reduction and taking the forward limit of the aforementioned 6D theories. Next, we study reformulating

S

-matrices in terms of the positive geometry, amplituhedron, which was first introduced to describe scattering in the 4D

\mathcal{N}=4

SYM theory. Similarly, We propose a positive geometry, called orthogonal momentum amplituhedron, to describe the tree-level scattering amplitudes of the 3D Chern-Simons matter theory (often termed ABJM theory). We study the co-dimension one boundaries and construct the canonical forms in this space of positive geometry.\\ \indent Recently, the integrated correlators of four BPS operators in the

\mathcal{N}=4

SYM theory were computed by the supersymmetric localisation. We show that in the perturbative regime, the integrated correlators are given by linear combinations of periods of certain conformal Feynman graphs. The periods involving multiple zeta values are of great interest in the study of mathematical physics and number theory. Finally, we study the four-point tree-level holographic correlators of arbitrary weights in the (2,0) supergravity theory on

AdS_3 \times S^3

, with two operators in tensor multiplet and the other two in gravity multiplet. We utilise the hidden 6D conformal symmetry, analogous to 10D symmetry for

AdS_5 \times S^5

, to arrive compact formulae in Mellin space. In the limits of maximally R-symmetry violating (MRV) limit and flat space, the formulae agree with results in other

AdS

backgrounds and the flat-space 6D amplitudes, respectively.

operator: BPS
R symmetry: violation
field theory: conformal
dimension: 6
multiplet: tensor
symmetry: conformal
correlation function
scattering amplitude
supergravity
geometry

References(214)

Figures(0)

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