David Berenstein, UCSB DPF 2015 Meeting Based on D.B., Eric Dziankowski, R
Spinning the fuzzy sphere David Berenstein, UCSB DPF 2015 meeting Based on D.B., Eric Dziankowski, R. Lashof Regas arXiv:1506.01722 This talk is not about this fuzzy sphere. Outline • Where the problem comes from and why it is interesting. • Ansatz for spinning fuzzy sphere and its consistency • Phase diagrams Holography Some large N field theories are equivalent to theories of quantum gravity in higher dimensions. Many solutions of such field theories have geometric interpretations, even at finite N Part of the goal is to find more examples of such solutions. SO(3) sector of BMN matrix model 1 1 3 H = Tr(P 2 + P 2 + P 2)+ Tr (Xj + i✏ XmXn)2 2 1 2 3 2 0 jmn 1 j=1 X @ A Has SO(3) symmetry with generator J = L = Tr(XP YP ) Z Y − X And a U(N) gauge invariance. Arises from • BMN matrix model (B,Maldacena, Nastase 2002) • Mass deformed N=4 SYM (Vafa, Witten; Polchinski, Strassler, …) • Equivariant Sphere reductions of Yang Mills on sphere (Kim, Klose, Plefka, 2003) Model is chaotic Yang Mills (on a box, with translationally invariant configurations) is chaotic. Basenyan, Matinyan, Savvidy, Shepelyanskii, Chirikov (early 80’) Chaos in BFSS matrix theory: Aref’eva, Medvedev, Rytchkov, Volovich (1998) Chaos in BFSS/BMN: Asplund, D.B., Trancanelli, Dzienkowski (2011,2012), Asano, Kawai, Yoshida (2015) The solutions with H =0aregivenbyfuzzyspheres.Thesearesolutionsoftheequations [Xi,Xj]=i✏ijkXk (6) The solutions to these equations are characterized by direct sums of the adjoint matrices for irreducible representations of su(2). For these solutions we have P1,P2,P3 =0andthusare classically gauge invariant according to (2).
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