Black Hole Quasinormal Modes and Seiberg–Witten Theory

We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $$\Omega $$ Ω -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.

Holographic M5 branes in AdS7 × S4

We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.

One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds

For scattering amplitudes in strong background fields, it is — at least in principle — possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds we consider this expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED and QCD. This enables us to obtain multicollinear limits of 1-loop vacuum amplitudes; the resulting helicity configurations are surprisingly restricted, with only the all-plus helicity amplitude surviving. These results are shown to be consistent with well-known vacuum amplitudes. We also show that for both abelian and non-abelian supersymmetric gauge theories, there is no helicity flip (and hence no vacuum birefringence) on any plane wave background, generalising a result previously known in the Euler-Heisenberg limit of super-QED.

The NSVZ relations for $$ \mathcal{N} $$ = 1 supersymmetric theories with multiple gauge couplings

We investigate the NSVZ relations for $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped SU(5) model, for which they easily reproduce the results for the two-loop β-functions. For $$ \mathcal{N} $$ N = 1 SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-like equation for the Adler D-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ β-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the β-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev-Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

Classification of large N superconformal gauge theories with a dense spectrum

We classify the large N limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor symmetry. We find 35 classes in total, with 8 having a dense spectrum of chiral gauge-invariant operators. The central charges a and c for the dense theories grow linearly in N in contrast to the N2 growth for the theories with a sparse spectrum. The difference between the central charges a − c can have both signs, and it does not vanish in the large N limit for the dense theories. We find that there can be multiple bands separated by a gap, or a discrete spectrum above the band. We also find a criterion on the matter content for the fixed point theory to possess either a dense or sparse spectrum. We discover a few curious aspects regarding supersymmetric RG flows and a-maximization along the way. For all the theories with the dense spectrum, the AdS version of the Weak Gravity Conjecture (including the convex hull condition for the cases with multiple U(1)’s) holds for large enough N even though they do not have weakly-coupled gravity duals.

Quantum simulation of gauge theory via orbifold lattice

We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.

Infinite-dimensional fermionic symmetry in supersymmetric gauge theories

We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $$ \mathcal{N} $$ N = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $$ \mathcal{N} $$ N = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.

Ambitwistor strings in six and five dimensions

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

Twisted 6d (2, 0) SCFTs on a circle

We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.