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Unravelling the Holomorphic Twist: Central Charges.

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November 2024

Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road, Oxford, OX2 6GG UK.

The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively.

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The superconformal index of half-BPS states in N=4 supersymmetric Yang-Mills with gauge group U(N) admits an expansion in terms of giant gravitons, I_{N}(q)=I_{∞}(q)∑_{m=0}^{∞}q^{mN}I[over ^]_{m}(q), where m is the number of giant gravitons and I_{∞}(q) is the graviton index. The expansion can be viewed as the implementation of trace relations for finite N. We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity.

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Coulomb Branch Amplitudes from a Deformed Amplituhedron Geometry.

Phys Rev Lett

May 2024

Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA and Institute for Particle and Nuclear Physics, Charles University in Prague, Prague, Czech Republic.

The amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us to propose a "deformed" amplituhedron.

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We study a family of higher-twist Regge trajectories in N=4 supersymmetric Yang-Mills theory using the quantum spectral curve. We explore the many-sheeted Riemann surface connecting the different trajectories and show the interplay between the degenerate nonlocal operators known as (near-)horizontal trajectories. We resolve their degeneracy analytically by computing the first nontrivial order of the Regge intercept at weak coupling, which exhibits new behavior: It depends linearly on the coupling.

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