Research
I am currently focusing my efforts on studying various aspects of higher spin particles and their connection with providing UV softness to observables. The Standard Model consists of particles of low spin: s = 0, 1/2, 1. These are the Higgs, leptons and quarks, photon and gluon and W and Z bosons, respectively. The graviton, with spin s = 2, completes the list of elementary particles. Particles with spin higher than 2 are mysteriously missing from this list.
Many no-go theorems about higher spin particles exist, stating that massless particles with spin higher than 2 cannot consistently interact with other particles at long distances in a way that respects relativity, equivalence principle, etc. A finite number of interacting massive higher spin particles also lead to causality issues.
Although higher spin particles have many theoretical challenges, the only known way currently to consistently formulate quantum gravity at high energies, string theory, incorporates an infinite tower of massive higher spins into the model. It is important therefore to understand the role higher spin particles play in formulating a UV complete gravity theory.
Selected Works
On the space of 2d integrable models (September 2024). We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond to the symmetry algebras of 2d integrable models. In this way, we initiate a systematic approach to mapping out the space of 2d integrable models. In the case of a single scalar, along with all subalgebras corresponding to known 2d integrable models, we find new mutually commuting subalgebras, which if infinite dimensional, define new integrable models.
Consistent actions for massive particles interacting with electromagnetism and gravity (September 2023) (published in JHEP Aug 9 2024). Consistent interactions between massive particles of any spin and electromagnetism/gravity are constructed at the Lagrangian level. This is achieved by preserving the covariantized massive gauge symmetry present in the free actions constructed below.
Covariant actions and propagators for all spins, masses and dimensions (July 2023) (published in Physical Review D Apr 15 2024). A new set of actions for free particles of any spin, mass, in any spacetime dimension is constructed, and their associated propagators are found. The massive spin n and n + 1/2 actions exhibit an interesting gauge symmetry, which will be used in an upcoming paper to solve the longstanding problem of finding consistent interactions of massive particles of spin higher than 1 with electromagnetism and gravity.
Generalized Veneziano and Virasoro amplitudes with Nicholas Geiser, (October 2022) (published in JHEP Apr 6 2023). We construct generalizations to the tree level open and closed string theory amplitudes, in an attempt to find UV complete alternatives. We recover the Coon amplitude as the (so far) unique alternative to the Veneziano amplitude, and we show that an analogous construction to generalize the Virasoro amplitude yields no alternative.
Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon with Nicholas Geiser, (July 2022) (published in JHEP Dec 19 2022). We study the properties of the only known alternative to the tree level string theory amplitudes which incorporate massive higher spins: the Coon amplitude. With an accumulation point spectrum, the Coon amplitude shows subtle non-meromorphic properties which affect the transcendental structure of the low energy expansion. An argument is given in the negative for the existence of a "double copy" of the Coon amplitude.
Searching for Gravity Without a Metric with E.T. Tomboulis, (July 2022). (published in Physical Review D Oct 18 2022) We study affine spacetime symmetry spontaneously broken down to the Lorentz group. This particular scenario has as a Goldstone boson the graviton. We for the first time construct an explicit affine invariant action which has an order operator that controls this symmetry breaking pattern. One can incorporate interactions to this action to study its symmetry breaking. A necessary feature of any theory of this sort is the appearance of an infinite tower of higher spin fields.