Dressed minimal surfaces in AdS4

Katsinis, Dimitrios; Manolopoulos, Dimitrios; Mitsoulas, Ioannis; Pastras, Georgios

doi:10.1007/jhep11(2020)128

Cited by 5 publications

(4 citation statements)

References 35 publications

(70 reference statements)

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“…Essentially, the non-linear superposition is the NLSM counterpart of the insertion of solitons in the Pohlmeyer reduced theory. In this spirit, our results, combined with the addition formula for the on-shell action derived in [5] enable the calculation of instanton contibutions over any classical configuration of the O(N ) NLSMs. It would be compelling to use this formalism in order to make contact with studies on the possible path integration contours for such models [21] or to discuss semi-classical quantization.…”

Section: Discussionmentioning

confidence: 82%

“…In our previous work [3] we solved these equations for g ∈ SO(3)/SO (2). This was achieved in a brute force manner, which was inspired by the application of the dressing method on elliptic strings in R × S 2 [4], as well as on the elliptic minimal surfaces in H 3 [5]. We introduced spherical coordinates and bootstrapped the solution of the auxiliary system using all the available equations.…”

Section: Introductionmentioning

confidence: 99%

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Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

Katsinis

2022

Preprint

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We show that the integrability of the SO(N )/SO(N −1) Principal Chiral Model (PCM) originates from the Pohlmeyer reduction of the O(N ) Non Linear Sigma Model (NLSM). In particular, we show that the Lax pair of the PCM is related upon redefinitions and identification of parameters to the zero curvature condition, which is a consequence of the flatness of the enhanced space used in the Pohlmeyer reduction. This identification provides the solution of the auxiliary system that corresponds to an arbitrary NLSM/PCM solution.

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Section: Discussionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

Katsinis

2022

Preprint

Self Cite

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“…a mapping to a system of coupled harmonic oscillators. This technique can be applied to compute M too [50], yielding closed-form formulas. Here we apply this method to the XY model in an external magnetic field (H) in the zero-temperature limit.…”

Section: B Low-temperature Expansion -Xy Model In a Magnetic Fieldmentioning

confidence: 99%

Machine-learning Iterative Calculation of Entropy for Physical Systems

Nir,

Sela,

Beck

et al. 2020

Preprint

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Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current methods for entropy estimation suffer either from a high computational cost, lack of generality or inaccuracy, and inability to treat complex, strongly interacting systems. In this paper, we present a novel method, termed MICE, for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine learning algorithm which works with arbitrary network architectures that can fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems, and identify the jamming point of a bidisperse mixture of soft spheres. Lastly, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.

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“…The above analysis demonstrates that the auxiliary system (1.2) is significant for many reasons. In our previous works we applied the dressing method for elliptic strings in R t × S 2 [67], see also [37], and elliptic minimal surfaces in H 3 [99]. One could proceed in a systematic manner and the only equations that had to be solved, were essentially solved by the seed solution upon altering some parameters.…”

Section: Introductionmentioning

confidence: 99%

Novel aspects of integrability for NLSMs in symmetric spaces

Katsinis

2022

Preprint

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We obtained the formal solution of the auxiliary system of Non Linear Sigma Models, whose target space is a rank 1 symmetric space based on the indefinite orthogonal group O(p, q), corresponding to an arbitrary solution of the NLSM. This class includes de Sitter, Anti-de Sitter and Hyperbolic spaces, which are of interest in view of the AdS/CFT correspondence. The formal solution is related to the Pohlmeyer reduction of the NLSM, constituting another link between the NLSM and the reduced theory. Besides deriving the solution, we also review the Pohlmeyer reduction of such models. Finally, we comment on the implications for the monodromy matrix and its eigenvalues.

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Dressed minimal surfaces in AdS4

Cited by 5 publications

References 35 publications

Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

Machine-learning Iterative Calculation of Entropy for Physical Systems

Novel aspects of integrability for NLSMs in symmetric spaces

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