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超対称行列量子力学の数値シミュレーション に基づくゲージ／重力対応の検証

超対称行列量子力学の数値シミュレーション に基づくゲージ／重力対応の検証. 共同研究者 : Konstantinos Anagnostopoulos （ Natl. Tech. U. , Athens ） 　　花田 政範（理研） 西村 淳（ KEK 総研大）. 発表者 : 竹内 紳悟 ( 総研大 ). Ref : Hanada-Nishimura-S.T. arXiv:0706.1647[hep-lat]

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超対称行列量子力学の数値シミュレーション に基づくゲージ／重力対応の検証

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  1. 超対称行列量子力学の数値シミュレーションに基づくゲージ／重力対応の検証超対称行列量子力学の数値シミュレーションに基づくゲージ／重力対応の検証 共同研究者 : Konstantinos Anagnostopoulos （Natl. Tech. U. , Athens） 　　花田 政範（理研） 西村 淳（KEK 総研大） 発表者 : 竹内 紳悟(総研大) Ref : Hanada-Nishimura-S.T. arXiv:0706.1647[hep-lat] Anagnostopoulos-Hanada-Nishimura-S.T. arXiv:0707.4454[hep-th] 基研研究会 「弦理論と場の理論 --- 量子と時空の最前線」 2007/8/6(月)-8/10(金)

  2. 0. Introduction Large-N supersymmetric gauge theories non-pert. formulation of superstring/M theories - BFSS matrix model and IIB matrix model Banks-Fischler-Shenker-Susskind ’97 Ishibashi-Kawai-Kitazawa-Tsuchiya ’97 - AdS/CFT and gauge/gravity duality Maldacena ’97 Itzhaki-Maldacena-Sonnenschein-Yankielowicz ’98 non-pert. study of superstring quantum description of BH

  3. 10d N=1 SYM Dim. Red. 1 dim. U(N) gauge theory with 16 supercharges non-pert. study of superstring/M theories (SUSY matrix quantum mechanics) Monte Carlo simulation (first principle study) -BFSS matrix model c.f.) Kabat-Lfschytz-Lowe ’01 Kawahara-Nishimura-S.T. in prep. -gauge/gravity duality Large-N limit N black D0 branes sol. in type IIA SUGRA low T strongly coupled

  4. Plan 0. Introduction 1. SUSY matrix QM with 16 supercharges 2. Non-lattice simulation for SUSY QM 3-1. Monte Carlo results --- Energy 3-2. Monte Carlo results --- Polyakov line 4. Summary and outlook

  5. 1. SUSY matrix QM with 16 supercharges 10d N=1 SYM Dim. Red. compactified bosonic fields : p.b.c. fermionic fields : anti p.b.c. MW fermion : temperature : effective coupling constant dual gravity low T strongly coupled high T weakly coupled high T exp. Kawahara-Nishimura-S.T. in prep.

  6. 2. Non-lattice simulation for 1d SUSY QM no need to use lattice the importance of lattice lies in its gauge inv. fixes the gauge sym. completely (specific to 1d) static diagonal gauge : no need to use lattice Fourier mode cutoff

  7. Advantages of the non-lattice simulation • theoretically clean the gauge-fixed action in the continuumexcept for a cutoff • restoration of SUSY(faster than lattice) • convergence to cont. lim.(faster than lattice) 1d WZ model 〇◇: non-lattice(our results) △▽ : lattice (Giedt et al) □ : lattice with half-SUSY (Catterall-Gregory) (16) (8) higher modes are suppressed by the kinetic term compensates superficial increase in computational efforts by factor

  8. 3. Monte Carlo results of energy from the dualtiy high T exp. from the dualtiy Predicted behavior sets in at T = 0.5 gauge/gravity duality (strongly coupled)

  9. Monte Carlo results of Polyakov line high T exp. deconfined phase gauge/gravity duality no phase transition (Barbon et al., Aharony et al.)

  10. 5. Summary and outlook • the first Monte Carlo results for the matrix QM with 16 supercharges low temp. (strong coupling region) non-lattice simulation method • evidences of gauge/gravity duality from first principles c.f.) Strominger-Vafa ’96 • no phase transition outlook • confirmation of gauge/gravity duality in lower temp. microscopic d.o.f. of BH • confirmation of gauge/string duality quantum behavior of BH

  11. c.f. ) Polyakov line (1d SYM with 4 supercharges) high T exp.

  12. c.f. ) Polyakov line (results of lattice) high T exp. (incl. next-leading) confined phase deconfined phase

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