Natalie M. Paquette

A bstract: In this note we initiate the study of “twisted holography” for the dualities involving the BFSS matrix quantum mechanics and the IKKT matrix model in their N → ∞ limits. We identify the admissible twists of each model, compute their cohomology in the BV-BRST formalism, and identify them — in the planar limit and in perturbation theory around the trivial background — with corresponding twists of IIA and IIB string theories, respectively. The twisted gravitational duals make manifest certain infinite dimensional symmetry algebras. In the BFSS example, the dual IIA supergravity twists are also obtained as certain zero mode truncations of the minimal (1/16-BPS) and maximal (1/4-BPS) twists of eleven-dimensional supergravity.

There is a special set of massless four-dimensional gauge theories which admit local and gauge-anomaly-free uplifts to twistor space; we call such theories twistorial. In twistorial theories, generalized towers of soft modes (including states of both helicities) form a 2d chiral algebra even at the quantum level. The 2d OPE limit of this chiral algebra coincides with the holomorphic collinear limit in 4d. This is true, in particular, for self-dual Yang–Mills theory coupled to special choices of matter, the latter being required to make the theory twistorial. Costello and the second author recently proposed that form factors of such twistorial 4d theories could be computed as 2d chiral algebra correlators. In turn, there exist form factors of self-dual theories, with insertions of appropriate local operators, that compute a subclass of observables in full (i.e. non-self-dual) QCD, coupled to appropriate matter. For example, the n-point two-loop all-plus QCD amplitude has recently been computed using the 1-loop chiral algebra OPEs determined thus far, but higher orders of the quantum-deformed chiral algebra must be determined to continue the ‘chiral algebra bootstrap’ program for higher-loop-level form factors of these twistorial theories. In this paper, using only elementary constraints from symmetries and associativity, we obtain closed-form expressions for the extended chiral algebra to arbitrary loop-order. This can be viewed as providing an all-loop result for a subset of collinear splitting functions in non-supersymmetric, massless QCD coupled to special choices of matter.

The recently devised chiral algebra bootstrap computes the form factors of a special class of “twistorial” 4d QFTs as correlation functions of the theory’s 2d celestial chiral algebra. Examples of twistorial theories include self-dual Yang-Mills theory coupled to special massless matter content, and certain form factors in these theories are equivalent to a subset of MHV amplitudes in massless QCD, coupled to the same matter. In this paper, we extend the chiral algebra bootstrap to include scattering in the presence of charged sources, using a self-dual dyon in a twistorial theory as our main example. Self-dual theories in the presence of such sources lift to holomorphic gauge theories on non-Hausdorff twistor space, and we generalize the Koszul duality construction of Costello and Paquette to this setting. With this approach, we easily reproduce a recent formula of Adamo, Bogna, Mason, and Sharma for n-point MHV scattering of gluons off the self-dual dyon.

In this work, we revisit and elaborate on twisted holography for AdS _3 × S^3 × X 3 × S 3 × X with X= T^4 X = T 4 , K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the N → ∞ N → ∞ , or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. This technique can in principle be used to compute corrections to the chiral algebra perturbatively in 1/N 1 / N .

The project on higher algebraic structures in algebra & holography showed that a mathematical subject called Koszul duality, which relates two kinds of algebraic structures to one another, can be understood as part of the famous holographic correspondence. It used a variation of these methods, further incorporating Penrose's twistor space, to equate the computation of certain four-dimensional amplitudes and form factors to correlation functions in a chiral algebra constructed from Koszul duality.

A bstract: We elaborate on various aspects of our top-down celestial holographic duality wherein the semiclassical bulk spacetime is a 4d asymptotically flat, self-dual Kähler geometry known as Burns space. The bulk theory includes an open string sector comprising a 4d WZW model and a closed string sector called “Mabuchi gravity” capturing fluctuations of the Kähler potential. Starting with the type I topological B-model on the twistor space of flat space, we obtain the twistor space of Burns space from the backreaction of a stack of N coincident D1 branes, while the chiral algebra is obtained from (a twist of) the brane worldvolume theory. One striking consequence of this duality is that all loop-level scattering amplitudes of the theory on Burns space can be expressed as correlation functions of an explicit 2d chiral algebra. We also present additional large- N checks, matching several 2 and 3-point amplitudes and their collinear expansions in the WZW ₄ sector, and the mixed WZW ₄ -Mabuchi sector, of the bulk theory to the corresponding 2 and 3-point vacuum correlators and operator product expansions in the dual chiral algebra. Key features of the duality, along with our main results, are summarized in the introduction.

We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at asymptotic null infinity, from the point of view of the 4d/2d twistorial correspondence introduced by Costello and the second author. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.

We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at asymptotic null infinity, from the point of view of the 4d/2d twistorial correspondence introduced by Costello and the second author. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.