We define a new correspondence for pairs <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$({\mathbb {F}},H)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">F</mi> <mo>,</mo> <mi>H</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> formed by a flag manifold <InlineEquation ID="IEq7"> <EquationSource Format="TEX">${\mathbb {F}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">F</mi> </math></EquationSource> </InlineEquation> together with an H-flux on <InlineEquation ID="IEq8"> <EquationSource Format="TEX">${\mathbb {F}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">F</mi> </math></EquationSource> </InlineEquation>. Given its role within our correspondence, infinitesimal T-duality may be viewed as a source of H-flux, in the sense that it contributes towards taking fluxless pairs <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$({\mathbb {F}},0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">F</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to pairs <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$({\mathbb {F}}^\vee , H^\vee )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">F</mi> </mrow> <mo>∨</mo> </msup> <mo>,</mo> <msup> <mi>H</mi> <mo>∨</mo> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> carrying nonzero flux <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$H^\vee \ne 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mo>∨</mo> </msup> <mo>≠</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We also illustrate how our correspondence exchanges complex structures with symplectic ones up to B-transformations.

The ${\textbf{H}}$-flux on flag manifolds generated by infinitesimal ${\textbf{T}}$-duality

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2026年6月26日

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Elizabeth Gasparim,
Lino Grama,
Carlos Varea

摘要

We define a new correspondence for pairs $({\mathbb {F}},H)$ $(F, H)$ formed by a flag manifold ${\mathbb {F}}$ $F$ together with an H-flux on ${\mathbb {F}}$ $F$ . Given its role within our correspondence, infinitesimal T-duality may be viewed as a source of H-flux, in the sense that it contributes towards taking fluxless pairs $({\mathbb {F}},0)$ $(F, 0)$ to pairs $({\mathbb {F}}^\vee , H^\vee )$ $(F^{\lor}, H^{\lor})$ carrying nonzero flux $H^\vee \ne 0$ $H^{\lor} \neq 0$ . We also illustrate how our correspondence exchanges complex structures with symplectic ones up to B-transformations.

The \({\textbf{H}}\)-flux on flag manifolds generated by infinitesimal \({\textbf{T}}\)-duality

摘要