1 / 20

Conformal field theories vs. SUSY gauge theories: the AGT conjecture

Conformal field theories vs. SUSY gauge theories: the AGT conjecture. A.Mironov Lebedev Physical Institute and ITEP. M-theory. projection. duality transformations. M-theory + Brane pictures. predictions. abstract. concrete. AdS/CFT ideology. AdS/CFT patterns

patsy
Download Presentation

Conformal field theories vs. SUSY gauge theories: the AGT conjecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Conformal field theories vs. SUSY gauge theories: the AGT conjecture A.Mironov Lebedev Physical Institute and ITEP

  2. M-theory projection duality transformations

  3. M-theory + Brane pictures predictions abstract concrete AdS/CFTideology • AdS/CFT patterns • Alday – Maldacena conjecture • Alday-Gaiotto-Tachikawa (AGT) • conjecture

  4. Conformal(2,0)6d theory Twisted compactification on a 2d Riemann surface 4d superconformal field theory Generalization of Witten’s M-theory construction of Seiberg-Witten theories

  5. AGT conjecture • Partition function of 4d N=2 superconformal gauge theory in -background in the low energy limit (=deformed Seiberg-Witten theory; = Nekrasov functions) • Conformal blocks in 2d conformal field theory (Lioville/Toda theory) • Matrix model with logarithmic potential (Dijkgraaf,Vafa; Mironov, Morozov, Shakirov)

  6. Basic example • N=2 SUSY 4d theory with U(2) gauge group and 4 fundamental matter hypermultiplets (beta-function is zero, the theory is conformal) • 4-point conformal block (in the Liouville theory)

  7. Seiberg-Witten theory Low energy effective action (pure gauge SU(2)): prepotential is v.e.v. of the scalar field - coupling constant

  8. perturbative contribution instantonic corrections Calculation of the instantonic contributions requires regularization -background

  9. Nekrasov functions Instead of instantons on , instantons on -background:

  10. =conformal block

  11. 2d conformal field theory • Energy-momentum tensor: • Virasoro algebra central charge

  12. Structure of operators • Primary fields: • Secondary fields: Conformal dimension

  13. Operator Product Expansion (OPE)

  14. Correlators etc

  15. Correlators - double ratio

  16. Conformal block

  17. AGT correspondence are linearly related with Checks and extensions

  18. AGT correspondence • Conformal block is universal, hence, AGT solves the problem of constructing generic conformal block • 3-point is not universal, Z_{pert}= Liouville 3-point function • Parametrization makes natural the free field approach. Hence, matrix models

  19. Thank you

More Related