Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines

Meltzer, Hagen

doi:10.1090/memo/0808

Cited by 59 publications

(89 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is the same as the OPE of N 2d complex scalars. Therefore the chiral algebra is given by the N complex scalars (in the adjoint of the gauge group) 46) with the central charge c 2d = 2N .…”

Section: Free Theoriesmentioning

confidence: 99%

See 1 more Smart Citation

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr M N where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A N . This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S 2 × T 2 where we turn on 1 2 N units of U(1) r flux on S 2 .

show abstract

Section: Free Theoriesmentioning

confidence: 99%

“…singularities allowed only if they may arise from quarks becoming massless). 15 These operators correspond to the mathematicians' telescopic (endo)functors in the corresponding derived category [46]. For a review in the present physical context, see [47].…”

Section: Jhep11(2017)013mentioning

confidence: 99%

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…For any B in mod R , we denote by ϒ F (B) the R ⊗ k -module being the middle term of the universal (in fact couniversal) extension η F B of B with respect to a fixed finite R-semisimple subcategory F of MOD R ⊗ k (if it exists, for the precise definitions and more details see Section 4.1, also [14,16] …”

Section: 1mentioning

confidence: 99%

“…provided μ(X) > μ (a slight generalization of [16,Corollary 5.2.3]). Observe that this formula allows to determine easily the slope μ(R(X)) for any indecomposable object X in C μ , for a fixed μ > μ.…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

“…Finally, we prove Theorem 3.2 being the heart of our algorithm and describing constructively elementary changes of parametrizing bimodules together with their control on the slope level. In the proof of this last result we apply the equivalence D b (mod ) D b (coh X) of the bounded derived categories, where coh X is the category of graded coherent sheaves over the weighted projective line X associated to , and moreover, the technique of tubular mutations (see [11,15,16]). …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Algorithm for the Construction of Parametrizing Bimodules for Homogeneous Modules Over Tubular Canonical Algebras

Dowbor

Meltzer

Mróz

2013

Algebr Represent Theor

Self Cite

View full text Add to dashboard Cite

show abstract

Higher S-dualities and Shephard-Todd groups

Cecotti

Zotto

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

Seiberg and Witten have shown that in N = 2 SQCD with N f = 2N c = 4 the S-duality group PSL(2, Z) acts on the flavor charges, which are weights of Spin (8), by triality. There are other N = 2 SCFTs in which SU(2) SYM is coupled to stronglyinteracting non-Lagrangian matter: their matter charges are weights of E 6 , E 7 and E 8 instead of Spin(8). The S-duality group PSL(2, Z) acts on these weights: what replaces Spin(8) triality for the E 6 , E 7 , E 8 root lattices?In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL(2, Z) factorizes trough the action of the exceptional ShephardTodd groups G 4 and G 8 which should be seen as complex analogs of the usual triality group S 3 ≃ Weyl(A 2 ). Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type.

show abstract

Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines

Cited by 59 publications

References 0 publications

Superconformal index, BPS monodromy and chiral algebras

Superconformal index, BPS monodromy and chiral algebras

An Algorithm for the Construction of Parametrizing Bimodules for Homogeneous Modules Over Tubular Canonical Algebras

Higher S-dualities and Shephard-Todd groups

Contact Info

Product

Resources

About