Matching the Hagedorn temperature in AdS/CFT correspondence

Harmark, Troels; Orselli, Marta

doi:10.1103/physrevd.74.126009

Cited by 46 publications

(166 citation statements)

References 50 publications

(177 reference statements)

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“…As we have seen, for strong coupling the characteristics of the thermodynamics of the spinor Bose gas at low temperatures are described by an effective ferromagnetic Heisenberg spin chain. There is a remarkable three-way correspondence [53,54] between the ferromagnetic Heisenberg chain, the limit of weakly coupled planar N = 4 supersymmetric Yang-Mills theory and the limit of free strings on AdS 5 × S 5 . This triality between guage theory, string theory and the thermodynamics of the ferromagnetic Heisenberg chain has recently been used to calculate the Hagedorn temperature of the string theory in agreement with the Hagedorn/deconfinement temperature calculated on the guage theory side [54].…”

Section: Discussionmentioning

confidence: 99%

“…There is a remarkable three-way correspondence [53,54] between the ferromagnetic Heisenberg chain, the limit of weakly coupled planar N = 4 supersymmetric Yang-Mills theory and the limit of free strings on AdS 5 × S 5 . This triality between guage theory, string theory and the thermodynamics of the ferromagnetic Heisenberg chain has recently been used to calculate the Hagedorn temperature of the string theory in agreement with the Hagedorn/deconfinement temperature calculated on the guage theory side [54]. It now appears that we can add a further connection with the thermodynamics of the strongly interacting two component spinor Bose gas.…”

Section: Discussionmentioning

confidence: 99%

“…Although there has been a wide range of interest in the ferromagnetic Heisenberg chain, realization of ferromagnet chains are relatively rare [52]. Most recent interest in the ferromagnetic Heisenberg chain has been from the perspective of string theory [53,54]. Obtaining exact analytical results for the thermodynamics of this model still provides a number of open challenges.…”

Section: Low Temperature Ferromagnetic Behaviourmentioning

confidence: 99%

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Ferromagnetic behavior in the strongly interacting two-component Bose gas

2007

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We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat cv ∼ T 1/2 and the susceptibility χ ∼ T −2 are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.PACS numbers: 03.75. Hh, 03.75.Mn, 04.20.Jb, 05.30.Jp I. INTRODUCTIONExperiments with ultracold quantum gases are opening up exciting new possibilities for testing and exploring quantum effects in many-body systems (for recent reviews, see Refs. [1][2][3]). These include experiments on effectively one-dimensional (1D) quantum Bose gases of 87 Rb atoms in which the interaction strength between atoms is tunable [4][5][6][7][8]. The experiments provide a striking example of realizing an integrable quantum many-body problem. They demonstrate the explicit fermionization of bosons and provide a direct test of theoretical results obtained for the integrable 1D interacting (spinless) Bose gas [9,10]. Another frontier of activity involves spinor Bose gases of alkali atoms in which hyperfine states comprise the pseudospins [11][12][13]. In these systems quantum collisional effects can produce spatio-temporal spin oscillations (spin waves) [14][15][16][17]. The observation of collective dynamics of spin waves and spin-state segregation in trapped spinor Bose gases has stimulated a wide range of interest in studying magnetism, topological spin defects and novel quantum phase transitions in spinor Bose gases [18,19]. Two-component spinor Bose gases have been experimentally created in a magnetic trap by rotating two hyperfine states so that the two atomic hyperfine states make up a pseudo-spin doublet [20], e.g., the |F = 2, m F = −1 and |F = 1, m F = 1 hyperfine states of 87 Rb. In general, spin-independent s-wave scattering dominates interactions in alkali atomic gases. In 1D, the two-component Bose gas with spin-independent s-wave scattering can be exactly solved, like the spinless model, by means of the Bethe ansatz [21,22]. In contrast to Fermi gases, ferromagnetic order emerges in spinor Bose gases as long as the interaction is fully spin independent [15,23]. The low-energy excitations of the model split into collective excitations carrying charge and collective excitations carrying spin. The charge...

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Low Temperature Ferromagnetic Behaviourmentioning

confidence: 99%

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Ferromagnetic behavior in the strongly interacting two-component Bose gas

2007

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“…27 It might be useful to make use of the Penrose limit [41] to examine the intermediate regime. See [50,51] for the comparison of the Hagedorn temperature.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Phase transitions of largeNorbifold gauge theories

Hikida¹

2006

J. High Energy Phys.

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We study the phase structures of N = 4 U (N ) super Yang-Mills theories on R × S 3 /Z k with large N . The theory has many vacua labelled by the holonomy matrix along the non-trivial cycle on S 3 /Z k , and for the fermions the periodic and the anti-periodic boundary conditions can be assigned along the cycle. We compute the partition functions of the orbifold theories and observe that phase transitions occur even in the zero 't Hooft coupling limit. With the periodic boundary condition, the vacua of the gauge theory are dual to various arrangements of k NS5-branes. With the anti-periodic boundary condition, transitions between the vacua are dual to localized tachyon condensations. In particular, the mass of a deformed geometry is compared with the Casimir energy for the dual vacuum. We also obtain an index for the supersymmetric orbifold theory. *

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“…also [27] and the references therein). However these topics are beyond the scope of our lecture notes which are oriented rather to cosmological applications.…”

Section: Pos(modave Viii)002mentioning

confidence: 99%

Thermodynamics of string gas

Liu¹

2013

Proceedings of Eighth Modave Summer School in Mathematical Physics — PoS(Modave VIII)

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Matching the Hagedorn temperature in AdS/CFT correspondence

Cited by 46 publications

References 50 publications

Ferromagnetic behavior in the strongly interacting two-component Bose gas

Ferromagnetic behavior in the strongly interacting two-component Bose gas

Phase transitions of largeNorbifold gauge theories

Thermodynamics of string gas

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