Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model

Chen-Te Ma

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Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model

Chen-Te Ma

High Energy Physics - Theory · Submitted 9 Feb 2015

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

The authors' main claim We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,727 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.41 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields. We perform the one-loop $\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints. The low energy theory can also be $O(D,D)$ invariant as the double sigma model. We use the other one way to construct different boundary conditions from the projectors. Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric. We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence. We show the one-loop $\beta$ function for the constant background fields and obtain the normal sigma model after integrating out the dual coordinates.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation.	background 0.54	0.33	0.20	asserted 1.00
s1	The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints.	background 0.59	0.37	0.06	asserted 1.00
s2	We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields.	contribution 0.57	0.91	0.09	asserted 1.00
s3	We perform the one-loop $\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints.	method 0.55	0.94	0.11	asserted 1.00
s4	The low energy theory can also be $O(D,D)$ invariant as the double sigma model.	result 0.85	0.52	0.18	hedged possibility 0.67
s5	We use the other one way to construct different boundary conditions from the projectors.	method 0.73	0.89	0.05	asserted 0.99
s6	Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric.	method 0.51	0.91	0.11	asserted 1.00
s7	We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence.	contribution 0.58	0.93	0.40	asserted 0.99
s8	We show the one-loop $\beta$ function for the constant background fields and obtain the normal sigma model after integrating out the dual coordinates.	result 0.95	0.93	0.29	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields. We perform the one-loop $\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints. The low energy theory can also be $O(D,D)$ invariant as the double sigma model. We use the other one way to construct different boundary conditions from the projectors. Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric. We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence. We show the one-loop $\beta$ function for the constant background fields and obtain the normal sigma model after integrating out the dual coordinates.

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5 arXiv papers cite this in 8 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 · 5 sentences without a confident label

Uses its method or tool 1 paper

We construct the Neumann and Dirichlet boundary conditions from the equivalence of the equations of motion by the self-duality relation [ref] .

Geometric Low-Energy Effective Action in a Doubled Spacetime · Open String Theory for One Doubled Space · 0.80

Cites it as background 2 papers

These days the exotic branes have been exhaustively investigated in the framework of supergravity theories [ref] , string worldsheet theories [ref] , worldvolume theories [ref] , extended geometries such as doubled sigma model and double field theory [ref] , $β$-supergravity and its extension [ref] , and other huge number of related works[Of course this classification is not rigorous because they are deeply related to each other.].

Semi-doubled Sigma Models for Five-branes · Introduction · 1.00
In the works [ref] boundary conditions are defined for a T(U)-duality covariant open string which on the one hand allows to calculate beta-function for (constant) background fields in the covariant formalism, and one the other hand to define Dp-branes as particular subspaces in the generalized doubled (exceptional) space.

The invariant action for solitonic 5-branes · Relation to other approaches · 0.96

What it cites · 22 sentences without a confident label

Uses the method or tool of 2 papers

The calculation is the same as [ref] .

One-Loop $\beta$ Function of the Double Sigma Model with Constant Background · Discussion and Conclusion · 0.87
We can follow [ref] to obtain the massless closed string theory from the bulk.

A Double Sigma Model for Double Field Theory · One-Loop $β$ Function for the Constant Background Fields · 0.88

Compares with 1 paper

It should have more different theoretical viewpoints than [ref] .

Gauge Transformation of Double Field Theory for Open String · Introduction · 0.89

Cites as support 1 paper

It exactly shows the low energy effective action of the generalized metric formulation [ref] .

Generalized metric formulation of double field theory · Introduction · 0.97

Cites as background 7 papers

They doubled coordinates (normal and dual coordinates) to embed the T-duality rule in the $O(D, D)$ structure for the closed string theory [ref] .

Double Field Theory · Introduction · 0.83
They doubled coordinates (normal and dual coordinates) to embed the T-duality rule in the $O(D, D)$ structure for the closed string theory [ref] .

The gauge algebra of double field theory and Courant brackets · Introduction · 0.83
They doubled coordinates (normal and dual coordinates) to embed the T-duality rule in the $O(D, D)$ structure for the closed string theory [ref] .

Generalized metric formulation of double field theory · Introduction · 0.83

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