The Potency of Nilpotence

ArXiv.org · 2025-12-03

The dynamics of $\mathcal{N}=1$ SUSY gauge theories with matter in adjoint and fundamental representations and the superpotentials given by Arnold's ADE singularities has been extensively studied in the literature. It was also conjectured that supersymmetric models with $W_{A_k}$, $W_{D_{k+2}}$ and $W_{E_7}$ superpotentials possess a dual description. In this paper we revisit the analysis of the moduli space of $A_k$ and $D_{k+2}$ models by considering the duality along nilpotent directions on the moduli space. While our analysis provides additional evidence for the duality conjecture in $W_{A_k}$ models, we show that the duality conjecture fails for the $W_{D_{k+2}}$ models.

Chirality Changing RG Flows: Dynamics and Models

arXiv (Cornell University) · 2023-03-15

Chirality plays an important role in understanding the dynamics of quantum field theories. In this paper, we study the dynamics of models where renormalization group flows change the chiral structure of the theory. We introduce model building tools and construct models with a variety of chirality flows: from the appearance of new massless composite matter, to the development of mass gaps to completely general changes in the chiral matter content. The stability of chirally symmetric vacua is sensitive to the interplay between non-perturbative dynamics and deformations necessary to generate chirality flows. In particular, we show that chirality flows can be easily induced by deformations of s-confining models. On the other hand, in the absence of true s-confinement, the required deformations destabilize chirally symmetric ground states.

Chirality changing RG flows: dynamics and models

Journal of High Energy Physics · 2023-06-26 · 1 citations

A bstract Chirality plays an important role in understanding the dynamics of quantum field theories. In this paper, we study the dynamics of models where renormalization group flows change the chiral structure of the theory. We introduce model building tools and construct models with a variety of chirality flows: from the appearance of new massless composite matter, to the development of mass gaps to completely general changes in the chiral matter content. The stability of chirally symmetric vacua is sensitive to the interplay between non-perturbative dynamics and deformations necessary to generate chirality flows. In particular, we show that chirality flows can be easily induced by deformations of s -confining models. On the other hand, in the absence of true s -confinement, the required deformations destabilize chirally symmetric ground states.

Pairwise Multiparticle States and the Monopole Unitarity Puzzle

Physical Review Letters · 2022-10-24 · 20 citations

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

Journal of High Energy Physics · 2021-08-01 · 2 citations

A bstract On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S -matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e 1 g 2 − e 2 g 1 , for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S -matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S -matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

Generation flow in field theory and strings

Journal of High Energy Physics · 2021-10-01

A bstract Nontrivial strong dynamics often leads to the appearance of chiral composites. In phenomenological applications, these can either play the role of Standard Model particles or lift chiral exotics by partnering with them in mass terms. As a consequence, the RG flow may change the effective number of chiral generations, a phenomenon we call generation flow. We provide explicit constructions of globally consistent string models exhibiting generation flow. Since such constructions were misclassified in the traditional model searches, our results imply that more care than usually appreciated has to be taken when scanning string compactifications for realistic models.

Monopoles Entangle Fermions

arXiv (Cornell University) · 2021-09-02 · 1 citations

We resolve the decades old mystery of what happens when a positron scatters off a minimal GUT monopole in an s-wave, first discussed by Callan in 1983. Using the language of on-shell amplitudes and pairwise helicity we show that the final state contains two up quarks and a down quark entangled with angular momentum stored in the gauge fields, which is the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our entanglement requires more than 2 dimensions.

Completing Multiparticle Representations of the Poincaré Group

Physical Review Letters · 2021-07-23 · 23 citations

We extend the definition of asymptotic multiparticle states of the $S$-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or ${q}_{ij}$, associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing ${q}_{ij}$, while for vanishing spins they reproduce Zwanziger's scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as ${q}_{ij}={e}_{i}{g}_{j}\ensuremath{-}{e}_{j}{g}_{i}$.

The axion mass from 5D small instantons

Journal of High Energy Physics · 2020-03-01 · 70 citations

A bstract We calculate a new contribution to the axion mass that arises from gluons propagating in a 5th dimension at high energies. By uplifting the 4D instanton solution to five dimensions, the positive frequency modes of the Kaluza-Klein states generate a power-law term in the effective action that inversely grows with the instanton size. This causes 5D small instantons to enhance the axion mass in a way that does not spoil the axion solution to the strong CP problem. Moreover this enhancement can be much larger than the usual QCD contribution from large instantons, although it requires the 5D gauge theory to be near the non-perturbative limit. Thus our result suggests that the mass range of axions (or axion-like particles), which is important for ongoing experimental searches, can depend sensitively on the UV modification of QCD.

UV sensitivity of the axion mass from instantons in partially broken gauge groups

Journal of High Energy Physics · 2020 · 69 citations

• Physics
• Particle physics
• Theoretical physics

A bstract We examine the contribution of small instantons to the axion mass in various UV completions of QCD. We show that the reason behind the potential dominance of such contributions is the non-trivial embedding of QCD into the UV theory. The effects from instantons in the partially broken gauge group appear as “fractional instanton” corrections in the effective theory. These will exhibit unusual dependences on the various scales in the problem whenever the index of embedding is non-trivial. We present a full one-instanton calculation of the axion mass in the simplest product group models, carefully keeping track of numerical prefactors. Rather than using a ’t Hooft operator approximation we directly evaluate the contributions to the vacuum bubble, automatically capturing the effects of closing up external fermion lines with Higgs loops. This approach is manifestly finite and removes the uncertainty associated with introducing a cutoff scale for the Higgs loops. We verify that the small instantons may dominate over the QCD contribution for very high breaking scales and at least three group factors.