Ramond-Ramond Fields, Cohomology and Non-Geometric Fluxes

Aaron Bergman; Daniel Robbins

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Ramond-Ramond Fields, Cohomology and Non-Geometric Fluxes

Aaron Bergman, Daniel Robbins

High Energy Physics - Theory · Submitted 26 Oct 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Given such a T-fold, we define the Z_2-graded cohomology theory describing the unquantized RR field strengths and discuss how the data of a T-fold can be interpreted in terms of generalized NSNS fluxes and the twisted differential of Shelton-Taylor-Wecht.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

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We consider compactifications of type II string theory in which a d-dimensional torus is fibered over a base X. In string theory, the transition functions of this fibration need not be simply diffeomorphisms of T^d but can involve elements of the T-duality group Spin(d,d,Z). We precisely define the notion of a T-fold with NSNS flux. Given such a T-fold, we define the Z_2-graded cohomology theory describing the unquantized RR field strengths and discuss how the data of a T-fold can be interpreted in terms of generalized NSNS fluxes and the twisted differential of Shelton-Taylor-Wecht.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider compactifications of type II string theory in which a d-dimensional torus is fibered over a base X.	background 0.76	0.38	0.03	asserted 0.93
s1	In string theory, the transition functions of this fibration need not be simply diffeomorphisms of T^d but can involve elements of the T-duality group Spin(d,d,Z).	background 0.99	0.09	0.08	asserted 0.69
s2	We precisely define the notion of a T-fold with NSNS flux.	contribution 1.00	0.93	0.11	asserted 1.00
s3	Given such a T-fold, we define the Z_2-graded cohomology theory describing the unquantized RR field strengths and discuss how the data of a T-fold can be interpreted in terms of generalized NSNS fluxes and the twisted differential of Shelton-Taylor-Wecht.	contribution 0.97	0.92	0.31	asserted 0.99

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Original abstract

We consider compactifications of type II string theory in which a d-dimensional torus is fibered over a base X. In string theory, the transition functions of this fibration need not be simply diffeomorphisms of T^d but can involve elements of the T-duality group Spin(d,d,Z). We precisely define the notion of a T-fold with NSNS flux. Given such a T-fold, we define the Z_2-graded cohomology theory describing the unquantized RR field strengths and discuss how the data of a T-fold can be interpreted in terms of generalized NSNS fluxes and the twisted differential of Shelton-Taylor-Wecht.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

M-theory and Type IIA Flux Compactifications
hep-th 2012-08 conditional novelty 7.0 of 10

New higher-derivative M-theory couplings involving fluxes and curvatures generate M5-brane charge, evading the supergravity no-go theorem and permitting Minkowski flux compactifications of M-theory and type IIA.
Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds
hep-th 2009-12 accept novelty 6.0 of 10

Flux compactifications of type IIB on SU(2)-structure orientifolds stabilize all moduli in AdS but are ruled out for de Sitter vacua and slow-roll inflation by new no-go theorems in all but one model, which itself giv...
On Slow-roll Moduli Inflation in Massive IIA Supergravity with Metric Fluxes
hep-th 2008-12 conditional novelty 6.0 of 10

For all but two of the standard toroidal orientifold compactifications of massive type IIA with metric fluxes, the slow-roll parameter epsilon is bounded below by a number of order one, excluding slow-roll inflation a...
de Sitter extrema and the swampland
hep-th 2018-07 conditional novelty 4.0 of 10

Over 400 de Sitter critical points are collected across a dozen classical type II flux compactification models, but none is shown to satisfy flux quantization at large volume and weak coupling.

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5 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Cites it as background 1 paper

See [ref] for some more mathematical aspects of this approach as well as a list of references and [ref] for some worked out examples in the context of type II flux compactifications.

de Sitter extrema and the swampland · Flux quantization · 0.98

What it cites · 27 sentences without a confident label

Uses the method or tool of 1 paper

In this section, we will describe a local description of this cohomology theory due to Atiyah and Segal [ref] in terms of open sets and transition functions.

Twisted K-theory and cohomology · Three legs on the base · 0.89

Compares with 4 papers

Also, the conditions on the fluxes obtained by requiring that $𝒟^2=0$, equivalently that the connection is flat, reproduce the Bianchi identities from the literature (see the computation of $𝒟^2$ in [ref] ).

Toroidal Orientifolds in IIA with General NS-NS Fluxes · One leg on the base · 0.86
Also, the conditions on the fluxes obtained by requiring that $𝒟^2=0$, equivalently that the connection is flat, reproduce the Bianchi identities from the literature (see the computation of $𝒟^2$ in [ref] ).

Generalized Flux Vacua · One leg on the base · 0.86
This agrees with with results already in the literature [ref] .

Towards Minkowski Vacua in Type II String Compactifications · One leg on the base · 0.97

Cites as background 4 papers

In the presence of a three-from NSNS background $[H] ∈H^3(X,)$, one can define a twisted K-theory group $K^∙_H(X)$ [ref] and a twisted cohomology group $H_H^∙(X)$ (the same as defined in section [ref]).

D-branes, B-fields and twisted K-theory · Discussion · 0.93
In the presence of a three-from NSNS background $[H] ∈H^3(X,)$, one can define a twisted K-theory group $K^∙_H(X)$ [ref] and a twisted cohomology group $H_H^∙(X)$ (the same as defined in section [ref]).

Twisted $K$-theory · Discussion · 0.93
We will begin by recalling some facts about $$, where $V$ is a real vector space of dimension $d$, largely following [ref] .

math.DG/0401221 · Clifford algebra actions · 0.98

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