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Hyperbolic string vertices
Published 2022-02-01“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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222
E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$ -Character Varieties: Branched Case
Published 2023-01-01“…For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!…”
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223
Hyperbolic string vertices
Published 2022“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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224
Hyperbolic string vertices
Published 2022“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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225
On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces
Published 2018“…These equations can be seen as real four-dimensional analogues of the Hitchin equations on Riemann surfaces, and one of common obstacles to be overcome is a certain unboundedness of solutions to these equations, especially of the “Higgs fields”. …”
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226
Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz
Published 2008“…We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. …”
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227
Mixed Hodge polynomials of character varieties
Published 2006“…We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. …”
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228
Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems
Published 2024-02-01“…Not only do we find that EPs can be intentionally shifted in parameter space by the saturable gain, but we also observe intriguing rotations and intersections of Riemann surfaces and find nonlinearity-enhanced sensing capabilities. …”
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229
Trinions for the 3d compactification of the 5d rank 1 E N f + 1 $$ {E}_{N_{f+1}} $$ SCFTs
Published 2023-06-01“…In this paper, we study compactifications of the rank 1 5d Seiberg E N f + 1 $$ {E}_{N_{f+1}} $$ SCFTs to 3d on Riemann surfaces of genus g > 1. We rely on the recent progress in the study of compactifications of 6d SCFTs to 4d and torus compactifications of 5d SCFTs to conjecture 3d N $$ \mathcal{N} $$ = 2 theories corresponding to the reduction of said 5d SCFTs on three punctured spheres. …”
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230
Quantum Jackiw-Teitelboim gravity, Selberg trace formula, and random matrix theory
Published 2020-12-01“…We show that the partition function of quantum Jackiw-Teitelboim (JT) gravity, including topological fluctuations, is equivalent to the partition function of a Maass-Laplace operator of large (imaginary) weight acting on noncompact, infinite-area, hyperbolic Riemann surfaces of arbitrary genus. The resulting spectrum of this open quantum system for a fixed genus is semiclassically exact and given by a regularized Selberg trace formula; namely, it is expressed as a sum over the lengths of primitive periodic orbits of these hyperbolic surfaces. …”
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231
Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT
Published 2016-09-01“…As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.…”
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232
Solving 3d gravity with Virasoro TQFT
Published 2023-10-01“…We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as "Virasoro TQFT". This TQFT is similar, but importantly not equivalent, to SL(2, $\mathbb{R}$) Chern-Simons theory. …”
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233
Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results
Published 2018“…Our exact results are expressed in terms of “excited-state” thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the Néel state, and we determine the first few non-analytic points.…”
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234
Entanglement and topology in RG flows across dimensions: caps, bridges and corners
Published 2023-04-01“…As concrete examples we discuss twisted compactifications of 4d N $$ \mathcal{N} $$ = 4 SYM on T 2, S 2 and hyperbolic Riemann surfaces.…”
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235
Entanglement and topology in RG flows across dimensions: caps, bridges and corners
Published 2023“…As concrete examples we discuss twisted compactifications of 4d <em>N</em> = 4 SYM on T<sup>2</sup>, S<sup>2</sup> and hyperbolic Riemann surfaces.</p>…”
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236
Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics
Published 2021-01-01“…Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. …”
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237
Bordered Heegaard Floer Homology and four-manifolds with corners
Published 2011Get full text
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238
Log-lightning computation of capacity and Green's function
Published 2021“…It also extends to "domains of negative measure" and other Riemann surfaces.…”
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239
Supersyrnmetric AdS(5) solutions of M-theory
Published 2004“…We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a 2-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T1,1/ℤ2. …”
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240
Weierstrass points on modular curves X0(N) fixed by the Atkin–Lehner involutions
Published 2023-01-01“…For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. …”
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