Analytic structure and explicit solution of an important implicit equation

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

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Explicit solution for the potential flow due to an assembly of stirrers in an inviscid fluid

Journal of Engineering Mathematics ◽

10.1007/s10665-008-9222-6 ◽

2008 ◽

Vol 62 (4) ◽

pp. 333-344 ◽

Cited By ~ 13

Author(s):

Darren Crowdy

Keyword(s):

Potential Flow ◽

Explicit Solution ◽

Inviscid Fluid

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Liquid power: reading the infinity pool as a global semioscape

Visual Communication ◽

10.1177/1470357220984823 ◽

2021 ◽

pp. 147035722098482

Author(s):

Crispin Thurlow

Keyword(s):

Digital Media ◽

Cultural Politics ◽

Primary Objective ◽

Analytic Structure ◽

Visual Texts ◽

Visual Material ◽

The World

The analytic focus of this article is the highly fashionable ‘infinity pool’, treated here as a visual-material realization of the cultural politics of super-elite mobility. The article is organized around a three-step analytic structure. First, I demonstrate how the infinity pool is mediatized as a status marker, and thus circulated and normalized. Second, I pinpoint the semiotic and ideological ways the infinity pool emerges as a mediated practice. Third, I examines how the infinity pool is also remediated on Instagram and thereby broadcast anew. Throughout, I evidence my analysis with visual texts drawn from a range of commercial, situated and digital media sources. My primary objective is to show how the infinity pool, as a mediatized, mediated and remediated practice, feeds the global semioscape, that more informal, often banal plane of cultural circulation where images, ideas and aesthetic ideals seed themselves all over the place. In this way, and however frivolous or innocuous infinity pools may seem, they also spread a particularly privileged way of looking at, and being in, the world.

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Resolving modular flow: a toolkit for free fermions

Journal of High Energy Physics ◽

10.1007/jhep12(2020)126 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Johanna Erdmenger ◽

Pascal Fries ◽

Ignacio A. Reyes ◽

Christian P. Simon

Keyword(s):

Complex Analysis ◽

Conformal Symmetry ◽

Standard Technique ◽

Analytic Structure ◽

Point Function ◽

Free Fermions ◽

Modular Evolution ◽

Non Local ◽

Kms Condition ◽

New Formula

Abstract Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

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