arXiv subjects

Subrabalan Murugesan

Publications and source records attributed to Subrabalan Murugesan.

3 recordsLinked to original sources

arXiv2026

Liouville Blocks from Spectral Networks

In this paper, we investigate the role of spectral networks in quantum Liouville theory, with particular emphasis on spectral networks of Fenchel-Nielsen-type. In the first part, we construct q-parallel transport for Fenchel-Nielsen networks through q-nonabelianisation, and compare with quantum parallel transport computed using the Moore-Seiberg formalism. This motivates a proposal for a quantum version of the NRS proposal. In the second part, we reproduce Liouville conformal blocks through the standard free-field formalism with Fenchel-Nielsen-type integration contours. However, we observe that this approach is not complete with respect to wall-crossing. We therefore develop an extension of the free-field formalism to smooth spectral coverings, with the Maulik-Okounkov R-matrix playing a central role. We conjecture that this new formalism generates the full spectrum of Liouville conformal blocks, and provides a first-principle definition for Goncharov-Shen conformal blocks.

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arXiv2025

Les Houches lectures on non-perturbative Seiberg-Witten geometry

In these lectures we detail the interplay between the low-energy dynamics of quantum field theories with four supercharges and the exact WKB analysis. This exposition may be the first comprehensive account of this connection and includes new arguments and results. The lectures start with the introduction of massive two-dimensional $\mathcal{N}=(2,2)$ theories and their spectra of BPS solitons. We place these theories in a two-dimensional cigar background with supersymmetric boundary conditions labelled by a phase $\zeta = e^{i \vartheta}$, while turning on the two-dimensional $\Omega$-background with parameter~$\epsilon$. We show that the resulting partition function $\mathcal{Z}_{\mathrm{2d}}^\vartheta(\epsilon)$ can be characterized as the Borel-summed solution, in the direction $\vartheta$, to an associated Schr\"odinger equation. The partition function $\mathcal{Z}_{\mathrm{2d}}^\vartheta(\epsilon)$ is locally constant in the phase $\vartheta$ and jumps across phases $\vartheta_\textrm{BPS}$ associated with the BPS solitons. Since these jumps are non-perturbative in the parameter~$\epsilon$, we refer to $Z^\vartheta_\mathrm{2d}(\epsilon)$ as the non-perturbative partition function for the original two-dimensional $\mathcal{N}=(2,2)$ theory. We completely determine this partition function $\mathcal{Z}^\vartheta_\mathrm{2d}(\epsilon)$ in two classes of examples, Landau-Ginzburg models and gauged linear sigma models, and show that $\mathcal{Z}^\vartheta_\mathrm{2d}(\epsilon)$ encodes the well-known vortex partition function at a special phase $\vartheta_\textrm{FN}$ associated with the presence of self-solitons. This analysis generalizes to four-dimensional $\mathcal{N}=2$ theories in the $\frac{1}{2} \Omega$-background.

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arXiv2024

Torus reduction of maximal conformal supergravity

We consider the dimensional reduction of N=(2,0) conformal supergravity in six dimensions on a two-torus to N=4 conformal supergravity in four dimensions. At the level of kinematics, the six-dimensional Weyl multiplet is shown to reduce to a mixture of the N=4 Weyl and vector multiplets, which can be reinterpreted as a new off-shell multiplet of N=4 conformal supergravity. Similar multiplets have been constructed in other settings and are referred to as dilaton Weyl multiplets. We derive it here for the first time in a maximally supersymmetric context in four dimensions. Furthermore, we present the non-linear relations between all the six- and four-dimensional bosonic and fermionic fields, that are obtained by comparing the off-shell supersymmetry transformation rules.

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