AdS5×S5Mirror Model as a String Sigma Model

Abstract

Doing a double Wick rotation in the worldsheet theory of the light cone AdS5 × S 5 superstring results in an inequivalent, so-called mirror theory that plays a central role in the field of integrability in AdS/CFT. We show that this mirror theory can be interpreted as the light cone theory of a free string on a different background. This background is related to dS5 × H 5 by a double T duality, and has hidden supersymmetry. The geometry can also be extracted from an integrable deformation of the AdS5 × S 5 sigma model, and we prove the observed mirror duality of these deformed models at the bosonic level as a byproduct. While we focus on AdS5 × S 5 , our results apply more generally.PACS numbers: 11.25.TqIntegrability has and continues to be of central importance in furthering our understanding of the AdS/CFT correspondence [1], giving important insights into finite coupling quantum field theory. Through fruitful interplay between results on both sides of the correspondence, remarkable progress has been made in the spectral problem in particular [2]. Namely, we can describe scaling dimensions in planar N = 4 supersymmetric Yang-Mills theory (SYM) at finite 't Hooft coupling through the corresponding energy levels of a string on AdS 5 × S 5 , and these energy levels can be computed exactly thanks to the integrability of the string [3]. More precisely, under the assumption that integrability persists at the quantum level, the spectrum of the AdS 5 × S 5 superstring can be determined by means of the thermodynamic Bethe ansatz applied to a doubly Wick rotated version of its worldsheet theory [4,5], as put forward in [6] and worked out in [7][8][9][10][11]. Since the light cone gauge fixed AdS 5 × S 5 string is not Lorentz invariant however, this double Wick rotation results in an inequivalent quantum field theory, the socalled mirror theory [7]. The associated mirror transformation also appears extensively in the exact description of polygonal Wilson loops or equivalently planar scattering amplitudes [12][13][14]. Given the central importance of the mirror theory, we would like to elevate it beyond the status of a technical tool. This raises a question that has gone unanswered since the model's introduction in 2007, namely whether the mirror theory itself can arise directly by light cone gauge fixing a free string on some background. Here we show that this is the case, giving an interesting relation between strings on different backgrounds different from other well known dualities. Our results extend to the integrable deformation of the AdS 5 × S 5 superstring of [15], show an intriguing link to de Sitter space, and indicate new backgrounds with hidden supersymmetry in the associated string sigma model. Our construction is based on a simple observation regarding the bosonic light cone string action that directly produces the desired 'mirror' metric for a fairly generic class of backgrounds. The doubly Wick-rotated light cone action is obtained by a formal exchange and inversion of the metric components of the two di...

Derivation of the action and symmetries of the q-deformed AdS5 × S 5 superstring

“…In particular, it was studied in [32] using the parameterization of [11], where it was found that the deformed metric in the limit κ → ∞ only corresponds to dS 5 × H 5 after applying some T -duality transformations. Furthermore, the same conclusion was reached more recently in [31] but with a different combination of T -dualities. What distinguishes the results of [32] and [31] is the way the various fields are scaled in the limit κ → ∞.…”

“…Furthermore, the same conclusion was reached more recently in [31] but with a different combination of T -dualities. What distinguishes the results of [32] and [31] is the way the various fields are scaled in the limit κ → ∞.…”

“…These results leave no doubt that the conclusion of [11] should extend to the full light-cone S-matrix. An interesting duality was also found in [30,31], relating the deformed superstring for two values of the deformation parameter η through mirror duality. It would be interesting to understand if such a duality admits a classical interpretation using the hamiltonian framework.…”

Poisson-Lie duals of the η deformed symmetric space sigma model

“…Various ways of taking this limit in the η deformed model have been studied [12,20,34,[52][53][54], with the limit of [52,53] having the particular algebraic interpretation as a contraction of the q deformed algebra [54].…”

Pulsating strings on (AdS3 × S3) ϰ

“…The deformed background breaks the symmetry of AdS 5 ×S 5 to [U(1)] 6 , which urges to the new insight of its dual field theory which has to be explored yet. In order to understand the various aspects of the background one can look in to [25][26][27][28][29][30][31][32][33][34]. The perturbative world sheet scattering matrix of bosonic particles of the model was computed in [25].…”