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Self-Dual Gauge Theory from the Top Down

Roland Bittleston, Kevin Costello, Keyou Zeng

Abstract

We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of $4d$ self-dual asymptotically flat backgrounds, and the large $N$ limit of an independently defined $2d$ chiral defect CFT. Our construction goes via twisted holography for the type I topological string on a Calabi-Yau five-fold which fibres over twistor space. In particular, we show that single-trace operators of the $2d$ defect CFT are in bijection with states of the celestial chiral algebra. We match the operator products of these states with the collinear splitting amplitudes of the self-dual gauge theory up to one-loop. Assigning vacuum expectations to central operators in the boundary theory computes bulk amplitudes on self-dual backgrounds. We are able to extract form factors from these amplitudes, which we use to give a simple closed formula for certain $n$-point two-loop all $+$ amplitudes in $\mathrm{SU}(K) \times \mathrm{SU}(R)$ gauge theory coupled to bifundamental massless fermions.

Self-Dual Gauge Theory from the Top Down

Abstract

We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of self-dual asymptotically flat backgrounds, and the large limit of an independently defined chiral defect CFT. Our construction goes via twisted holography for the type I topological string on a Calabi-Yau five-fold which fibres over twistor space. In particular, we show that single-trace operators of the defect CFT are in bijection with states of the celestial chiral algebra. We match the operator products of these states with the collinear splitting amplitudes of the self-dual gauge theory up to one-loop. Assigning vacuum expectations to central operators in the boundary theory computes bulk amplitudes on self-dual backgrounds. We are able to extract form factors from these amplitudes, which we use to give a simple closed formula for certain -point two-loop all amplitudes in gauge theory coupled to bifundamental massless fermions.

Paper Structure

This paper contains 78 sections, 5 theorems, 496 equations, 22 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Self-Dual QCD
  3. Twistor Uplifts of SDQCD
  4. Integrability of SDQCD and the Twistorial Anomaly
  5. Review of Celestial Chiral Algebras
  6. SDQCD from String Theory
  7. Turning on Background Fields
  8. From Physical to Topological Strings
  9. Connections with the Witten-Berkovits Twistor String
  10. Amplitude Computations
  11. The Algebra on the Defect
  12. BRST Cohomology at Large N
  13. Bulk States
  14. Backreaction
  15. Computing OPEs using Feynman Diagrams
  16. ...and 63 more sections

Key Result

Lemma 1

There is only one Feynman diagram that connects two $\phi$ operators, which is the one described above. Similar statements hold for the $\gamma-\widetilde{\gamma}$, $\mathrm{b}-\mathrm{c}$ propagator. There is no Feynman diagram that connects other pairs of fields.

Figures (22)

  • Figure 1: Tree gluon diagrams leading to collinear splitting in form factors
  • Figure 2: This figure depicts a two-loop diagram with external gluons in $\mathfrak{sp}(K)$ and a gluon exchange in $\mathfrak{sl}(R)$. The $\mathfrak{sl}(R)$ gluons are represented by photon propagators with arrows indicating the flow of helicity.
  • Figure 3: Diagrammatic representation of the gluon states $\mathds{J}_{IJ}[k,l]$ and $\widetilde{\mathds{J}}_{IJ}[k,l]$
  • Figure 4: Planar and non-planar terms in the $\phi-\phi$ propagator, emitting two $\partial_{w_i}\mathrm{c}$ fields. There are further contributions from the $\partial_{w_i}\mathrm{c}$ fields attaching to the other side of the propagator.
  • Figure 5: A fairly generic Feynman diagram, including $\phi-\phi$ propagators (blue lines) and a $\psi-\psi$ propagator (dashed line). Since the gauge group is $\mathfrak{sp}(N)$, the $\phi-\phi$ propagator can be a twisted propagator in double line notation, as drawn. Each $\phi-\phi$ propagator emits two $\partial_{w_i}\mathrm{c}$ fields.
  • ...and 17 more figures

Theorems & Definitions (12)

  • Conjecture 1
  • Lemma 1
  • proof
  • Proposition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Conjecture 2
  • Conjecture 3
  • ...and 2 more