Thermodynamic bubble ansatz

By L. Alday, D. Gaiotto, J. Maldacena. 2009

259 citations recorded by the source corpus.

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fa8787db8f8d438383b10293a947a4e42f97eca2

How researchers see this paper

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In Condensed Matter Physics

1. A. Sever
2. P. Vieira
3. D. Gaiotto
4. L. Dixon
5. J. Drummond
6. J. Maldacena
7. L. Alday
8. M. Hippel

In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. J. Drummond
4. J. Maldacena
5. N. Arkani-Hamed
6. P. Vieira
7. A. Sever
8. L. Alday

Citations in the corpus

• Motivic amplitudes and cluster coordinates (2013, background): “Finally, we have so far made no explicit reference to the integrability of planar SYM theory (see the review [79]), which clearly plays a crucial but so far not fully exploited part in unlocking the structure of its amplitudes (approaches other than the OPE mentioned above include for example [80–83”
• Y-system for scattering amplitudes (2010, methodology): “One can give an alternative derivation of this formula in the spirit of the one given in [15] for the n = 6 case.”
• From correlation functions to Wilson loops (2010, background): “7) in [32]) and putting it together with the other nonconformal piece Adiv, we can produce a manifestly conformal “remainder”, which is the one-loop value of the factorWconformal from (4.”
• Heptagons from the Steinmann cluster bootstrap (2016, methodology): “The utility of the BDS-like ansatz was first noticed in the strong coupling analysis of amplitudes via the AdS/CFT correspondence [92] (see also ref.”
• Hexagon functions and the three-loop remainder function (2013, methodology): “On the diagonal line (u, u, u), we observed that the two-loop, three-loop, and strongcoupling [64] remainder functions are almost indistinguishable in shape for 0 < u < 1.”
• The four-loop six-gluon NMHV ratio function (2015, background): “Such a quantity has already been considered in the analysis of the strong-coupling behavior of amplitudes [92], as well as in the study of the multi-particle factorization limit of the NMHV amplitude [39].”
• An operator product expansion for polygonal null Wilson loops (2010, methodology): “Finally, in appendices E and F we give a new form for the integral equations described in [ 15 , 16].”
• Framed BPS states (2010, unknown): “They are useful because they provide a neat way to compute hyperkähler metrics on M, because they provide a framework within which one can prove the Kontsevich-Soibelman wall-crossing formula [5], and because they can be used to construct scattering amplitudes inN = 4 theories at strong coupling [6,”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “In the same line of thought, it is conceivable that there is a very direct link between the Yangian structure we uncovered and the very beautiful connections made at strong coupling with integrable systems, Y-systems, TBA equations and the Yang-Yang functional [79,80].”
• Scattering of massless particles: scalars, gluons and gravitons (2013, background): “Thus we can define Rm ≡ ui,i+m, and by a simple change of variable Rm = Ym 1+Ym the equations in terms of the new variables become precisely the Y-system equations in the high temperature limit considered in [21],”
• Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, background): “This result was already matched with the strong coupling minimal area computation of the hexagon Wilson loop [32] in [3].”
• Wall-crossing in coupled 2d-4d systems (2011, methodology): “Recently the methods of [1, 2] have found some surprising applications to scattering in N = 4 super Yang-Mills theory [82, 83, 84, 85].”
• Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, background): “One additional point of data for scattering amplitudes is their value at strong coupling [40, 64, 65].”