arXiv subjects

Shehab Hossam Fadda

Publications and source records attributed to Shehab Hossam Fadda.

4 recordsLinked to original sources

arXiv2026

Revisiting Schrödinger CFTs: Factorization, Massless Particles, and a Path to the Bootstrap

We revisit Schrödinger CFTs from a modern point of view. We introduce the ''harmonic trap geometry,'' analogous to the cylinder picture in relativistic CFTs, and demonstrate a state-operator correspondence that applies to all operators, including descendant, massless, and ''normal-ordered operators.'' A thermofield double construction plays an extremely important role. We systematically classify all physical spectra in the harmonic trap and their unitarity bounds, extending earlier results to include both massless and massive states of all spins, providing a new analytic treatment of unitarity bounds, and establishing foundations for a bootstrap. In our reformulation, previously known perturbative non-renormalization theorems follow immediately from non-perturbative factorization at fixed points and along RG flows. Massless states are described by an effective 1d CFT, as predicted by DLCQ, and violate the non-renormalization theorems. We include a self-consistent review of Schrödinger CFTs in our framework, making the paper accessible to anyone with a field theory background.

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arXiv2026

Observables in Schrödinger CFTs: How Aliens Built the Pyramids

We discuss the algebraic structure of observables in Schrödinger CFTs. These operators have zero mass (or particle number) and generically transform in staggered ''pyramid representations'' built from ''alien operators,'' as we explain with the doubled state-operator correspondence. We comment on implications for the space of non-relativistic CFTs, thermal physics, and generalize the exceptional symmetry conservation laws of Bekaert, Meunier, and Moroz, and Golkar and Son. We show that alien operators are analogous to double-twist operators in Lorentzian CFT, with systematic cross-channel corrections from massless particles when they exist.

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arXiv2026

Mirror symmetry on a circle

We investigate the small circle, or high temperature, limit of the supersymmetric index identities for the three-dimensional abelian mirror symmetry of SQED. There exist two possible limits, depending on how the parameters of the theory are scaled with the radius of the circle. In both cases the result is qualitatively similar. One side always reduces to the sphere partition function of a two-dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model (GLSM). The opposite side has a two-fold interpretation, either as the sphere partition function of the Landau--Ginzburg (LG) model that is Hori--Vafa dual to the GLSM, or as a Coulomb gas integral for a correlation function of Liouville or Toda CFT. This approach thus provides a systematic way to generate integral identities between partition functions of GLSMs on the one hand, and partition functions of LG models or CFT Coulomb gas integrals on the other. The latter perspective finds useful applications in the recently proposed 2d/2d correspondence, which relates sphere partition functions of unitary 2d $\mathcal{N}=(2,2)$ theories and correlation functions of non-unitary 2d CFTs that both descend from compactifications of a unitary 4d $\mathcal{N}=2$ SCFT. We present an example based on the $(A_{k-1},A_{N-1})$ Argyres--Douglas theories, where the CFT is a non-unitary minimal model. We also give a purely two-dimensional derivation of the identities obtained in the small circle limit which is inspired by the Kapustin--Strassler piecewise derivation of 3d abelian mirror symmetry.

hep-th↗

arXiv2026

Cardy limit of the 3d superconformal index

We study the superconformal index $Z(q)$ of 3d $\mathcal{N}=2$ gauge theories in Cardy-like limits $β= \log \tfrac{1}{q} \to 0^+$, extending techniques recently developed in the 4d $\mathcal{N}=1$ context. For theories with vectorlike matter content we find on the first sheet ($q \to 1$) that $Z(q) \sim β^{-\#}$, where the exponent $\#$ is determined by a $multiscale\ decomposition$ of the BPS moduli space appearing in the localization formula for the index. On the second sheet ($q \to e^{2πi})$ we find $Z(q) \sim e^{\#/ β}$, and that the long-standing puzzle of apparent gauge-enhancing saddles is resolved (in the absence of Chern--Simons couplings) via a novel $Lorentzian\ factorization$ formula that establishes complete screening. A key insight is the use of $Poisson\ resummation$, which streamlines the asymptotic analysis, sharpens the link to Kaluza--Klein effective field theory, and provides a dual description of parts of the BPS moduli space in terms of punctured surfaces. The Lorentzian factorization formula also emerges from Poisson resummation, though applied after a contour crossing in moduli space. This, in turn, hints at a correspondence between 3d monopoles and vortices via 2d duality.

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