We calculate the $\textit{θ}$ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is $$ \mathcal{N} $$ = 2 SU(2) gauge theory with $\textit{N}$ = 0, 1, 2, 3 flavors of fundamentals, explicitly broken to $$ \mathcal{N} $$ = 1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchy $\textit{m}$ ≪ $\textit{μ}$ ≪ Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function of $\textit{θ}$ which undergoes 1st order phase transitions between different vacua where the various dyons condense. For $\textit{N}$ = 0 we find the expected phase transition at $\textit{θ}$ = $\textit{π}$, while for $\textit{N}$ = 1, 2, 3 we find phase transitions at fractional values of $\textit{π}$.

United States

Csaba Csáki

Japan

Teruhiko Kawano

Hitoshi Murayama

Israel

Ofri Telem

Phase transitions at unusual values of $\textit{θ}$

We calculate energy correlators in a general holographic model of confinement, involving an asymptotically anti-de Sitter (AdS) warped extra dimension. Building on a recent computation in a minimal hard-wall model of confinement, we show that the shockwave method for efficiently computing energy correlators in AdS generalizes to an arbitrary warped geometry. This is possible because exact, linear shockwave solutions to the 5D field equations exist in any warped background. We apply our formalism to compute the two-point energy correlator for two simple models of confinement with interesting infrared spectra — one with a gapped continuum spectrum and one with linear Regge trajectories. The results differ from the simple hard-wall model and from each other, demonstrating that the details of the confining dynamics affect the shape of the energy correlator observables.

Steven Ferrante

Ameen Ismail

Holographic energy correlators for soft walls

We propose a model that provides a simultaneous solution to the doublet-triplet splitting problem of grand unified theories, the electroweak hierarchy problem and the strong CP problem. The mechanism is based on the dynamics of two axion-like particles that would crunch the universe at the time of the QCD phase transition if triplets were light or had a VEV or if doublets were heavy or did not have a VEV. The only trace left at low energies are these two axion-like particles. They are weakly coupled to the Standard Model and could be detected at upcoming axion experiments or by a combination of neutron EDM measurements and the astrophysical detection of fuzzy dark matter.

France

Raffaele D’Agnolo

Eric Kuflik

Pablo Sesma

A cosmological solution to the doublet-triplet splitting problem

We examine the phase structure of a QCD-like theory at   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  = π obtained from supersymmetric SU(N) QCD perturbed by a small amount of supersymmetry breaking via anomaly mediation (AMSB QCD). The spectrum of this theory matches that of QCD at the massless level, though the superpartners are not decoupled. In this theory it is possible to nail down the phase structure at   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  = π as a function of the quark masses and the number of flavors F. For one flavor we find that there is a critical quark mass, below which CP is unbroken, while above the critical mass CP is spontaneously broken. At the critical mass there is a second-order phase transition along with a massless η  ′ . We are able to analytically solve for the minima and the critical mass for N = 2, 3 as well as for the large N limit, while for other N one can find numerical results. For two flavors, we find that CP is always broken as long as the quark masses are equal and non-zero, however there is a non-trivial phase boundary for unequal quark masses, which we find numerically. For F ≥ 3 we obtain an intricate phase boundary which reproduces the various quark mass limits. All our results are in agreement with the predictions of refs. [1–5] for ordinary QCD that were based on anomaly matching arguments for generalized symmetries and the effective chiral Lagrangian. We also briefly comment on the domain wall solutions first discussed by Draper [6], and are able to present analytic results for the simplest case of SU(2) with one flavor.

Maximilian Ruhdorfer

South Korea

Taewook Youn

Spontaneous CP breaking in a QCD-like theory

It is usually assumed that 4$\textit{D}$ instantons can only arise in non-Abelian theories. In this paper we re-examine this conventional wisdom by explicitly constructing instantons in an Abelian gauge theory: $\textit{QED}$ with $\textit{N}$ flavors of Dirac fermions, in the background of a Dirac monopole. This is the low-energy effective field theory for fermions interacting with a ’t Hooft-Polyakov monopole, in the limit where the monopole is infinitely heavy (hence pointlike) and static. This theory, whose non-topological sectors were studied by Rubakov and Callan, has a far richer structure than previously explored. We show how to calculate the topological instanton number, demonstrate the existence of ’t Hooft zero modes localized around such instantons, and show how instantons in the path integral provide the underlying mechanism for the Callan-Rubakov process: monopole-catalyzed baryon decay with a cross section that saturates the unitarity bound. Our computation relies on correctly identifying the relevant 2$\textit{D}$ EFT for monopole catalysis as $\textit{Axial QED}$ in an effective $\textit{AdS}$ metric.

Rotem Ovadia

John Terning

Shimon Yankielowicz

Abelian instantons and monopole scattering

We present a holographic calculation of energy correlators in a simple model of confinement based on a warped extra dimension with an IR brane. For small distances we reproduce the constant correlators of a strongly-coupled conformal field theory, while for large distances the effects of confinement dominate and the correlators decay exponentially. We find exact shockwave solutions to the Einstein equations in the presence of the IR brane, hence avoiding the need for a perturbative expansion in terms of Witten diagrams. While some of the expected qualitative features of energy correlators in quantum chromodynamics (QCD) are reproduced, our crude model of confinement does not capture the effects of asymptotic freedom nor exhibit jetty behavior. We expect that our method can also be applied to more realistic models of confinement incorporating asymptotic freedom, which should fix some of the deviations from QCD.

Holographic energy correlators for confining theories

We study representations of the Poincaré group that have a privileged transformation law along a <math><mi>p</mi></math>-dimensional hyperplane, and uncover their associated spinor-helicity variables in <math><mi>D</mi></math> spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of <math><mi>S</mi><mi>O</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo></math>, the symmetry group of the <math><mi>p</mi></math>-hyperplane. We will refer to our generalized states as “partially celestial.” Following Wigner’s method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor-helicity variables for every <math><mi>D</mi></math> and <math><mi>p</mi></math>, we are able to construct the little group covariant part of partially celestial amplitudes. Finally, we briefly examine the application of the pairwise little group to partially celestial states with mutually nonlocal charges.

Partially celestial states and their scattering amplitudes

We present a simple set of power counting rules which allows us to easily estimate calculable instanton effects up to   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1) factors. We apply the resulting Instanton NDA to examine the effects of small instantons on various axion models. We confirm that mechanisms that increase the axion mass via small instantons generically also lead to an enhancement of misaligned instanton contributions to the axion potential, deepening the axion quality problem. For generic models, new sources of CP violation in the UV must be absent in order to raise the axion mass above the QCD prediction. However, we find that Z N  and composite axions are UV-safe against these misalignment effects. Axion GUT models are also insensitive to UV contributions at the GUT scale, unless a very large number of extra states are introduced below this scale.

Instanton NDA and applications to axion models

We investigate the dynamics responsible for generating the potential of the η  ′ , the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the θ angle, and that this same potential largely determines the properties of the η  ′  once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N − F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F &lt; N – 1, and in the dual gauge group for F &gt; N + 1. For the special cases of F = N – 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1) R  symmetry. We find that the η  ′  mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the η  ′  potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

India

Rick Gupta

Tuhin Roy

On the dynamical origin of the η ′ potential and the axion mass

We propose a simple modification of the Goldberger-Wise mechanism for stabilizing the scale of spontaneously broken conformal theories. The source of explicit conformal symmetry breaking is a relevant operator with a small coefficient, as opposed to the usual mechanism of an almost marginal operator with an order-one coefficient. In the warped 5D picture this relevant stabilization corresponds to a small tadpole for the bulk scalar on the UV brane, which can be technically natural if it is the only source for the breaking of a symmetry (for example, a discrete Z 2). This modification of the stabilization mechanism has significant consequences for the nature of the conformal phase transition, since the radion/dilaton potential is no longer shallow. The bounce action is significantly reduced, leading to a weaker first-order phase transition instead of the supercooled and strongly first-order transition seen in Goldberger-Wise stabilization. This also leads to reduction of gravitational wave signals which, however, may still be observable at future detectors. We present numerical and analytical studies of the phase transition and the resulting gravitational wave signal strength, assuming that the effective dilaton potential provides a good leading approximation. While the dilaton is not expected to be generically light in this setup, in order to keep perturbative control over the effective theory one needs to mildly tune the dilaton quartic to be somewhat small.