Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

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Spectral curves are transcendental

Letters in Mathematical Physics ◽

10.1007/s11005-020-01349-y ◽

2021 ◽

Vol 111 (1) ◽

Author(s):

H. W. Braden

Keyword(s):

Spectral Curve ◽

Spectral Curves ◽

Arithmetic Properties ◽

A Charge

AbstractSome arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if smooth.

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Classical spectral curve of the AdS5 × S5 lambda superstring

Journal of High Energy Physics ◽

10.1007/jhep05(2020)010 ◽

2020 ◽

Vol 2020 (5) ◽

Author(s):

Timothy J. Hollowood ◽

J. Luis Miramontes ◽

Dafydd Price

Keyword(s):

Spectral Curve

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Decentralized Particle Filter With Arbitrary State Decomposition

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2010.2091639 ◽

2011 ◽

Vol 59 (2) ◽

pp. 465-478 ◽

Cited By ~ 27

Author(s):

Tianshi Chen ◽

Thomas B. Schon ◽

Henrik Ohlsson ◽

Lennart Ljung

Keyword(s):

Particle Filter ◽

Arbitrary State

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Remote operations and interactions for systems of arbitrary-dimensional Hilbert space: State-operator approach

Physical Review A ◽

10.1103/physreva.65.032312 ◽

2002 ◽

Vol 65 (3) ◽

Cited By ~ 44

Author(s):

Benni Reznik ◽

Yakir Aharonov ◽

Berry Groisman

Keyword(s):

Hilbert Space ◽

Operator Approach ◽

State Operator ◽

Dimensional Hilbert Space ◽

Space State ◽

Remote Operations

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Differentiation of Vulnerable Carotid Plaques by Analysis of Calcium Content and Spectral Curve Slope using Gemstone Spectral Imaging

10.21203/rs.3.rs-515069/v1 ◽

2021 ◽

Author(s):

Ze-Xin Fan ◽

Xiao-Qing Li ◽

Ting-Ting Yang ◽

Shao-Jie Yuan ◽

Tian-Tong Niu ◽

...

Keyword(s):

Atherosclerotic Plaque ◽

Carotid Plaque ◽

Spectral Curve ◽

Plaque Rupture ◽

Spectral Imaging ◽

Calcium Content ◽

Carotid Atherosclerotic Plaque ◽

Close Link ◽

Gemstone Spectral Imaging ◽

Hs Crp

Abstract Growing evidence indicates that vulnerable carotid plaque rupture is an important cause of stroke. However, fewer studies have been conducted to investigate the role of a novel gemstone spectral imaging (GSI) in assessment of vulnerable carotid plaque. In this study, we analyzed GSI data including calcium content of carotid atherosclerotic plaque and spectral curve slope, as well as serum high-sensitivity C-reactive protein (Hs-CRP), monocyte chemotactic protein-1 (MCP-1) levels in patients with carotid atherosclerotic plaque using the GSI-computed tomographic angiography (CTA) and immunoturbidimetry. The patients with unstable plaques demonstrated a significantly lower calcium content and higher spectral curve slope than the stable plaques group. In addition, the patients with unstable plaque showed an increase in Hs-CRP levels and MCP-1 levels compared with the stable plaque and normal controls (NC) group. The alternation in GSI calcium content and spectral curve slope reflects a close link between calcification and plaque instability, while derangement of Hs-CRP and MCP-1 is involved in the formation or development of vulnerable plaques. Taken together, our results strongly support the feasibility of using these serological and newly discovered imaging parameters as multiple potential biomarkers relevant to plaque vulnerability or stroke progression.

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