The Gauge-String Duality and Heavy Ion Collisions

Abstract

I review at a non-technical level the use of the gauge-string duality to study aspects of heavy ion collisions, with special emphasis on the trailing string calculation of heavy quark energy loss. I include some brief speculations on how variants of the trailing string construction could provide a toy model of black hole formation and evaporation. This essay is an invited contribution to “Forty Years of String Theory” and is aimed at philosophers and historians of science as well as physicists.

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Notes

  1. 1.

    The remarks quoted in the first two paragraphs come from various sources. “Theory of everything” came to early prominence in [1]. String theory’s development is characterized as backward in [2]. The phrase “string miracles” occurs in [3]. Witten’s remark appeared in print in [4]. Townsend’s quote hasn’t appeared in print as far as I know, and it is more properly understood as the closest paraphrase that my memory can provide. The expression “Not even wrong” is apparently due to Pauli, but its application to string theory is most prominent in [5]. “The Trouble with Physics” is the title of [6]. Wilczek’s quote appeared in [7].

  2. 2.

    It is striking that early explorations [20] of what became the membrane paradigm of black hole horizons revealed essentially the same result for the shear viscosity as found in [19]. But the interpretation of that early work is obscured by the existence of a negative (and so apparently unphysical) bulk viscosity. Also, the horizons considered in [20] are of finite extent, which obstructs the hydrodynamic limit. In any case, the context of the gauge-string duality, together with the motivation from heavy-ion physics to be explained below, make clear the proper physical interpretation of the result, as well as its importance.

  3. 3.

    Strictly speaking, the spin 1 particles of \({\mathcal{N}}=4\) super-Yang-Mills theory are generalized gluons, in the sense that physically observed gluons are particles associated with the SU(3) gauge symmetry of QCD, whereas the gluons of \({\mathcal{N}}=4\) super-Yang-Mills are associated with an SU(N) gauge invariance, with N arbitrary at this stage.

  4. 4.

    Collisions of protons on protons are also common, and the LHC focuses on this type of collision.

  5. 5.

    Nevertheless there is a robust effort to describe many facets of the initial state and early stages of the collision using a combination of perturbative and semi-classical methods. In addition to [26], see for example the reviews [27, 28].

  6. 6.

    I would be remiss not to note that there are QCD calculations, both in perturbative and partially perturbative frameworks, which have made impressive headway on the problem of describing rapid energy loss. For an introductory review of these methods, see for example [36].

  7. 7.

    Viscosity also relates to a time-dependent situation, where a fluid has some non-trivial motion (shearing flow, for example) which damps out over time at a rate that the viscosity controls. For viscosity (as well as other transport properties) a standard approach is to extract an appropriate transport coefficient from a two-point correlator, which represents a perturbation of a uniform, static system. In principle, lattice QCD practitioners can get at the appropriate two-point functions, and the effort to do so for viscosity has had some success [47]. So the point is not that lattice QCD cannot possibly get at the quantities that string theorists compute; rather, it’s that string theorists have, at least temporarily, the advantage of a simpler and more nearly analytically tractable approach.

  8. 8.

    The sense in which this must happen is that signals on the parts of the worldsheet where v(r)<v 0 have no choice but to propagate further away from the string endpoint. This is a simple version of the notion of an apparent horizon.

  9. 9.

    There is a significant caveat to this statement: one could imagine a situation where for arbitrarily late times, there is always some part of the string worldsheet, however small it may be, which cannot send a signal to the endpoint of the string. Such a situation would be like a black hole remnant. To rule out such a possibility, one could impose the constraint that the string ends on a brane which is deep down in the bulk.

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Gubser, S.S. The Gauge-String Duality and Heavy Ion Collisions. Found Phys 43, 140–155 (2013). https://doi.org/10.1007/s10701-011-9613-9

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Keywords

  • Gauge-string duality
  • Heavy ion collisions
  • String theory