Higher Spin Gravity and Entanglement Entropy
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1 Hgher Spn Gravty and Entanglement Entropy Eva Llabres Llambes Supervsor: Alejandra Castro Unverstet van Amsterdam 4 February 2015 Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
2 Introducton and Motvaton Hgher spn theores are extensons of pure gravty coupled to an nfnte tower of massless spn felds. They are formulated n an AdS background, and they have hghly non lnear equatons of moton. Why Hgher Spn Gravty? AdS/CFT Why 2+1 dmensons? No propagatng degrees of freedom. Chern Smons theores SL(N, R SL(N, R Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
3 Introducton and Motvaton Why Entanglement Entropy? S EE = L X 4 G 3 No geometry for hgher spn theores Ryu-Takayanag proposal not vald Could we fnd an emergent "geometry" for hgher spn theores from entanglement entropy? Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
4 Gravty as Chern-Smons theory S CS [A] = k 4π G = SL(2, R SL(2, R, Tr (A da + 23 A A A A, Ā SL(2, R: Pure gravty s Chern-Smons S EH = S CS [A] S CS [Ā] G = SL(N, R SL(N, R, A, Ā SL(N, R: Chern-Smons s hgher spn gravty, wth a truncated tower of hgher spns (s = 2, 3,... N Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
5 Holographc Entanglement entropy and Wlson lnes Wlson lne s entanglement entropy for pure gravty (A, Ā SL(2, R [Ammon-Castro-Iqbal 13]: W R (f, = Tr R (A + Ā lenght geodesc = EE CONJECTURE: Wlson lne s EE for hgher spn (A, Ā SL(N, R: CHECKS: - Wlson loop reproduces thermal entropy of hgher spn black holes. - Results for specfc hgher spn background expected from CFT. Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
6 Holographc Entanglement entropy and Wlson lnes Wlson lne s entanglement entropy for pure gravty (A, Ā SL(2, R [Ammon-Castro-Iqbal 13]: W R (f, = Tr R (A + Ā Endponts CFT lenght geodesc = EE CONJECTURE: Wlson lne s EE for hgher spn (A, Ā SL(N, R: CHECKS: - Wlson loop reproduces thermal entropy of hgher spn black holes. - Results for specfc hgher spn background expected from CFT. Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
7 Holographc Entanglement entropy and Wlson lnes Wlson lne s entanglement entropy for pure gravty (A, Ā SL(2, R [Ammon-Castro-Iqbal 13]: W R (f, = Tr R Infnte-Dm Hghest-Weght (A + Ā Endponts CFT lenght geodesc = EE CONJECTURE: Wlson lne s EE for hgher spn (A, Ā SL(N, R: CHECKS: - Wlson loop reproduces thermal entropy of hgher spn black holes. - Results for specfc hgher spn background expected from CFT. Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
8 The problem of the two proposals [deboer-jottar 13] [Ammon-Castro-Iqbal 13] ( S EE k log lm ρ 0 Wcomp R (f, [ ( ( ] W R comp (f, = TrR P exp Ā P exp A f S EE = log (W R (f, W R (f, = Tr R (A + Ā THE TWO PROPOSALS ARE THE SAME!!! Castro-Llabres 14 [arxv: [hep-th]] Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
9 The problem of the two proposals [deboer-jottar 13] [Ammon-Castro-Iqbal 13] ( S EE k log lm ρ 0 Wcomp R (f, S EE = log (W R (f, W comp R ( (f, = Tr R [P exp ( ] Ā P exp A f W R (f, = Tr R (A + Ā 2 N(N 1/2 dmensonal THE TWO PROPOSALS ARE THE SAME!!! Castro-Llabres 14 [arxv: [hep-th]] Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
10 The problem of the two proposals [deboer-jottar 13] [Ammon-Castro-Iqbal 13] ( S EE k log lm ρ 0 Wcomp R (f, S EE = log (W R (f, W comp R ( (f, = Tr R [P exp 2 N(N 1/2 dmensonal ( ] Ā P exp A f W R (f, = Tr R Infnte-Dmensonal Hghest-Weght (A + Ā THE TWO PROPOSALS ARE THE SAME!!! Castro-Llabres 14 [arxv: [hep-th]] Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
11 The problem of the two proposals [deboer-jottar 13] [Ammon-Castro-Iqbal 13] ( S EE k log lm ρ 0 Wcomp R (f, S EE = log (W R (f, W comp R ( (f, = Tr R [P exp 2 N(N 1/2 dmensonal ( ] Ā P exp A f W R (f, = Tr R Infnte-Dmensonal Hghest-Weght (A + Ā THE TWO PROPOSALS ARE THE SAME!!! Castro-Llabres 14 [arxv: [hep-th]] Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
12 Wlson lne Parallel transport operator: Gauge transfomaton: ( P exp dx µ A µ ( ( P exp dx µ A µ G 1 (f P exp dx µ A µ G( A G 1 (A+dG Wlson lne: ( ] W R (C f = Tr R [P exp dx µ A µ Eva Llabres (UvA Hgher Spn Theores and EE 4 February / 6
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