Holomorphic structure of massive scalar fields in (A)dS_2 with Calvin Y.-R. Chen and Massimo Porrati (January 2026). We study a special set of scalar fields in two dimensional (Anti-)de Sitter space which, despite having a mass, still exhibit a holomorphic splitting of its solution space. As a result, these theories have a large algebra of local and non-linear symmetries, which we study and use to find integrable deformations.

Constraining all possible Korteweg-de Vries type hierarchies (February 2025). (published in Physical Review D Oct 6 2025). We continue the study of infinite dimensional mutually commuting subalgebras present in the massless scalar theory in 2d. These subalgebras define integrable deformations of the massless scalar, which are generalizations of the Korteweg-de Vries equation. We find new necessary conditions on these subalgebras, which ultimately narrow in on the space of all possible integrable hierarchies of the Korteweg-de Vries type.

On the space of 2d integrable models (September 2024) (published in JHEP Jan 28 2025). 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.

Dealing with Ghosts in Higher Derivative Theories 

Entanglement Entropy 

Examples of Anomaly Inflow 

Non-Perturbative Version of the Non-Renormalization Theorem