A Panorama Of Physical Mathematics c. 2022

Bah, Ibrahima; Freed, Daniel S.; Moore, Gregory W.; Nekrasov, Nikita; Razamat, Shlomo S.; Schäfer‐Nameki, Sakura

doi:10.48550/arxiv.2211.04467

Cited by 5 publications

(8 citation statements)

References 1,120 publications

(1,423 reference statements)

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“…= e 2π i a 8 , a = 1, 3, 5, 7 (5.26) σ 3 , σ 5 and σ 7 generate three Z 2 subgroups of the full Galois group. These subgroups fixes the following subfields of F G = Q(i, √ 2).…”

Section: 23mentioning

confidence: 99%

“…Quantum field theories have led to the discovery of new mathematical structures, and have given us deep insights into several areas of mathematics. Some examples include the study of low-dimensional topology using Chern-Simons theory [1][2][3], the discovery of mirror symmetry from string theory [4], the discovery of vertex operator algebras from conformal field theory [5][6][7] and many more [8].…”

Section: Introductionmentioning

confidence: 99%

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Row–column duality and combinatorial topological strings

Padellaro,

Radhakrishnan,

Ramgoolam

2024

J. Phys. A: Math. Theor.

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Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on Dijkgraaf-Witten theories of flat G-bundles for finite groups G in two dimensions, denoted G-TQFTs. We define analogous combinatorial topological strings related to two dimensional TQFTs based on fusion coefficients of finite groups. These TQFTs are denoted as R(G)-TQFTs and allow analogous integrality results to be derived for partial row sums of characters over conjugacy classes along fixed rows. This relation between the G-TQFTs and R(G)-TQFTs defines a row-column duality for character tables, which provides a physical framework for exploring the mathematical analogies between rows and columns of character tables. These constructive proofs of integrality are complemented with the proof of similar and complementary results using the more traditional Galois theoretic framework for integrality properties of character tables. The partial row and column sums are used to define generalised partitions of the integer row and column sums, which are of interest in combinatorial representation theory.

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“…= e 2π i a 8 , a = 1, 3, 5, 7 (5.26) σ 3 , σ 5 and σ 7 generate three Z 2 subgroups of the full Galois group. These subgroups fixes the following subfields of F G = Q(i, √ 2).…”

Section: 23mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Row–column duality and combinatorial topological strings

Padellaro,

Radhakrishnan,

Ramgoolam

2024

J. Phys. A: Math. Theor.

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“…They describe universal macroscopic behaviors of many-body quantum or statistical systems, ranging from critical Ising model, fractional quantum hall systems to quantum gravity via holography principle. Exact results in TQFTs and supersymmetric CFTs (SCFTs) have triggered the currently ongoing explosion in the area of physical mathematics, see [1] for a recent nice review on the subject.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the rank-0 SCFT turns out to contain a pair of non-unitary (semi-simple) TQFTs, say TFT ± in a Coulomb/Higgs branch limit [2]. 1 The (rank-0 SCFT)/(non-unitary TQFTs) correspondence provides a novel classification scheme of rank-0 SCFTs by studying its associated non-unitary TQFTs. Using the correspondence, for example, one can derive a lower bound on F (round 3-sphere free-energy) for N = 4 rank-0 SCFTs [2].…”

Section: Introductionmentioning

confidence: 99%

Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

Gang

Kim

2023

J. High Energ. Phys.

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By applying the recently proposed (3D rank-0 $$ \mathcal{N} $$ N =4 SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an exotic class of non-unitary TQFTs labelled by an integer k ≥ 3. The SCFTs are obtained by gauging diagonal SU(2) subgroup of T[SU(2)] theory with Chern-Simons level k. We give the explicit expression for modular data, S and T matrices, of the TQFTs. When k = 4m2 + 4m + 3 with an integer m ≥ 1, the modular data (modulo a decoupled semion) is identical to a non-unitary Haagerup-Izumi modular data. Thus, we give a physical realization of the exotic non-unitary modular data as well as its generalization using an exotic class of SCFTs.

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“…Broadly, we may classify the subjects in two groups, as reflected by the different parallel session talks at this conference: Formal aspects of Quantum Field Theories (QFT) and Quantum Aspects of Gravity. Recent progress is summarised in [4,5] and [6] respectively.…”

Section: Introductionmentioning

confidence: 99%

Formal theory: status and outlook

Quevedo¹

2022

Proceedings of 41st International Conference on High Energy Physics — PoS(ICHEP2022)

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A very brief overview is presented on some of the current most active areas of research in formal aspects of High Energy Physics and Cosmology. Including the recent breakthrough on the black hole information paradox, developments on amplitudes, the bootstrap and swampland programmes as well as progress towards realistic UV complete models of particle physics and cosmology. Perspectives on future contact with observations are discussed emphasising the long term prospect for ultra high frequency gravitational waves to test early universe physics beyond the Standard Model.

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A Panorama Of Physical Mathematics c. 2022

Cited by 5 publications

References 1,120 publications

Row–column duality and combinatorial topological strings

Row–column duality and combinatorial topological strings

Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

Formal theory: status and outlook

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