Antun Milas’s research while affiliated with University at Albany, State University of New York and other places

... The first two properties were mentioned above and are quite natural from the perspective that the bulk TQFT arises from twisting a rank-0 SCFT. The notion of classical freeness was first introduced in [45,46] in the computation of chiral homology groups, see also [47,48] for further developments and examples, but is quite rare and still not well understood physically or mathematically. There is evidence that the VOAs coming from 4d N = 2 SCFTs must be classically free, e.g. the only classically free minimal models are the M (2, 2r + 3) [45] and these are precisely the ones realized by Argyres-Douglas theories of type (A 1 , A 2n ) [36]. ...

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Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs

... Calinescu et al. [4] also proved the conjecture for r = 2 which coincides with Zagier's third rank two example listed in [21, Table 2]. Recently, Milas and Wang [10] proved this conjecture for r = 3 by establishing some Rogers-Ramanujan type identities for the corresponding Nahm sums. As the rank increases, evaluating the tadpole Nahm sums becomes much more complicated, which makes the conjecture difficult when r ≥ 4. ...

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Modularity of tadpole Nahm sums in ranks 4 and 5

... Finally, we note that if Q is obtained from a simple graph G by "doubling" (putting an arrow i → j whenever i and j are connected by an edge), the algebra A Q may be interpreted as the coordinate algebra of the arc space [19,31] of the variety defined by quadratic monomials corresponding to edges of G. Those algebras are studied in the recent papers [7,8,20,26,27] with lattice vertex algebras as one of the main tools. It would be desirable to examine the algebras A Q for other quivers in the context of the study of relationships between arc spaces and vertex algebras [1]. ...

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Koszul algebras and Donaldson–Thomas invariants

... These are not typically identifiable with a classical integrable model, and in all the cases we have checked there are no local conserved charges, apart from one exception, the (1,4) perturbation in M (2,11). In this particular case the chiral algebra can be identified with the degeneration of the W G 2 chiral algebra to at c = −232/11 to the Virasoro algebra [52], and the (1, 4) perturbation can be identified as related to d ...

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Non-local charges from perturbed defects via SymTFT in 2d CFT

... For example, Hikami's variant of the Andrews-Gordon identities [11], n i+1 + δ a,i n i = (q a+1 , q 2m−a , q 2m+1 ; q 2m+1 ) ∞ (q) ∞ , valid for m ≥ 2 and 0 ≤ a ≤ m − 1, can be proved using the theory of Bailey pairs, as can several other similar families of infinite product and false theta identities, [11,16,17]. Identities involving products of q-binomial coefficients similar to (1.13) also arose in connection with Schur's indices of certain 4d N = 2 Argyres-Douglas theories in [12]. For t ≥ 1, 1 ≤ s ≤ t + 1 define (with the convention that n t+1 = 0): D t,s = n 1 ,··· ,nt≥0 q ns t r=1 q nrn r+1 +nr (q) 2 nr . ...

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Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee

... The property (B), which is good modular transformation property, is proved by Matsusaka-Terashima [MT21] for Seifert homology spheres and Bringmann-Mahlburg-Milas [BMM20] for non-Seifert homology spheres whose surgery diagrams are the H-graphs. Their works are based on the results by Bringmann-Nazaroglu [BN19] and Bringmann-Kaszian-Milas-Nazaroglu [BKMN21], which clarified and proved the modular transformation formulas of false theta functions. ...

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A Proof of a Conjecture of Gukov–Pei–Putrov–Vafa

... Recently, Gukov-Pei-Putrov-Vafa [21] introduced important q-series called homological blocks for any plumbed 3-manifolds associated with negative definite plumbing tree graphs based on Gukov-Putrov-Vafa [20]. A physical viewpoint strongly suggests that the homological blocks have several interesting properties [6][7][8][9][11][12][13][14][15]19,22,31]. In particular, it is expected that the homological blocks have good modular transformation properties and their special limits at root of unity are identified with the Witten-Reshetikhin-Turaev (WRT) invariants. ...

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Modular Transformations of Homological Blocks for Seifert Fibered Homology 3-Spheres

... Finally, we note that if Q is obtained from a simple graph G by "doubling" (putting an arrow i → j whenever i and j are connected by an edge), the algebra A Q may be interpreted as the coordinate algebra of the arc space [19,31] of the variety defined by quadratic monomials corresponding to edges of G. Those algebras are studied in the recent papers [7,8,20,26,27] with lattice vertex algebras as one of the main tools. It would be desirable to examine the algebras A Q for other quivers in the context of the study of relationships between arc spaces and vertex algebras [1]. ...

Reference:

Koszul algebras and Donaldson–Thomas invariants

... (n) is a simple vertex algebra and the following holds: [21], [6]) where f sh is a short nilpotent element of sl(4). ...

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ON SOME VERTEX ALGEBRAS RELATED TO V−1sln AND THEIR CHARACTERS

... Let V + c (ns) be the fixed point vertex subalgebra. It is proved in [21,25] that V + c (ns) is a W -algebra of type W (2, 4, 6). ...

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On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds