logging in or signing up Verlinde Gulkund Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINTLite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 129 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: November 28, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript A Farey Tail for Attractor Black Holes: A Farey Tail for Attractor Black Holes Strings 2006 Beijing, June 24 Based on work with Jan de Boer, Miranda Cheng, Robbert Dijkgraaf en Jan ManschotOutline: Outline Black hole Farey tail: Rademacher series exact Cardy formula. AdS/CFT interpretation: sum over BTZ-black holes “dressed” with (virtual) particles (Farey tail) Attractor Black Holes: BPS states and Spectral flow MSW (0,4)-SCFT: generalized Elliptic genus. N=2 Farey Tail: relation with the OSV-conjecture. Rademacher Series: Rademacher Series => Exact Cardy FormulaProof:: Proof: Position of poles labeled by rational ratio’s c/d: They can ordered by the size of the denominator: Farey series. pole AdS3/CFT2: AdS3/CFT2 geometries have torus with modulus t as boundary.Thermal AdS3: Thermal AdS3 Periodic identification => non-contractible time circle BTZ black holeFarey tail: Z(t)= sum over SL(2,Z) orbit of black holes: Farey tail: Z(t)= sum over SL(2,Z) orbit of black holes contribution of each black hole geometry subleading corrections: black hole ‘dressed’ with light particle states that do not form black holesA Farey tail for BPS black holes: A Farey tail for BPS black holes Original example: D1D5 system on K3xT2 => N=4 black holes. Z(t,y) = elliptic genus of symmetric product of K3. (DMMV) New example: M5-M2 on CY => N=2 attractor black holes. Z(t,y) = elliptic genus of (0,4) SCFT of MSW. Crucial property: factorizability in terms of theta-functions. M5 and M2 branes on CY. : M5 and M2 branes on CY. M5-brane wraps a 4-cycle in CY => 5d black string Near-horizon geometry becomes Volume of CY and AdS radius are free. 5d gauge fields M2-brane charges M-theory on CY Is symmetry of M-theory!(0,4) CFT and 4d black holes : (0,4) CFT and 4d black holes Wrapped M5-brane reduces to wound string => D4-branes Momentum along string: D0-charge 6d (2,0) theory => (0,4) 2d CFT Chiral bosons => lorentzian metric Lorentzian lattice M2 => D2-charge Rightmoving superconformal algebra: SU(2) current algebra Degenerate groundstate due to goldstino zeromodes (cf. RR states) M-theory on CY x S 1 Maldacena, Strominger, WittenElliptic genus and BPS black holes: Elliptic genus and BPS black holes Gaiotto, Strominger, Yin The OSV partition function equals the elliptic genus More precisely one should compute removes bosonic and fermionic zeromodes follows from spectral flow! Denef, MooreRademacher formula for characters: Rademacher formula for characters For with Slide13: Farey tail for attractor black holes: Tail described by gas of M2 and anti-M2 branes: For large charges described by topological strings! but truncated to respect “no-BH bound”. => GV & OSV Cf. talks by Yin, Dijkgraaf, Denef, Strominger….Conclusions : Conclusions Farey tail gives an exact correspondence between microscopic state counting and macroscopic black hole configurations, but not one to one. It applies to N=4 and N=2 black holes, but central concept should hold more generally. N=2 case required absence of D6-branes. Can one put those back in? Is there a “universal” elliptic genus with a product formula like in N=4? What are its duality properties? Spectral flow, Sp(2b-2,Z) are suggestive. Can one understand truncation of spectrum from non-perturbative approach to topological strings? You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.