Open-Closed Correspondence of K-theory and Cobordism

Blumenhagen, Ralph; Cribiori, Niccolò

doi:10.48550/arxiv.2112.07678

Cited by 5 publications

(12 citation statements)

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“…log y , (A. 13) where we have set an integration constant to zero without loss of generality. We recover the equivalent to (2.18), albeit with a and δ kept independent.…”

Section: A Local Dynamical Cobordisms With Curved (D − 1)-dimensional...mentioning

confidence: 99%

“…1 Such end-of-the-world configuration may correspond to a boundary (such as the 10d Horava-Witten boundary of 11d M-theory [2,3]), a bubble of nothing in which some compactification space shrinks to zero size [4] (see [5][6][7][8] for some recent works), or more exotic possibilities, and may possibly be dressed with charged objects, such as branes, orientifold planes or generalizations (dubbed I-folds in [9]). The cobordism conjecture, already at this topological level, has produced interesting results, see [6,[9][10][11][12][13] for some references. 2 An exploration of the Cobordism Conjecture beyond the topological level was undertaken in [21,22] via the study of spacetime varying solutions to the equations of motion in theories with dynamical tadpoles, namely, potentials which do not have a minimum and thus do not admit maximally symmetric solutions (see [23][24][25][26] for early work and [27][28][29][30] for related recent developments, and [31,32] for a complementary approach to cobordism solutions).…”

Section: Jhep06(2022)142 1 Introductionmentioning

confidence: 99%

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At the end of the world: Local Dynamical Cobordism

Angius

Calderón-Infante

Delgado

et al. 2022

J. High Energ. Phys.

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The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world ‘branes’. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric USp(32) theory, Bubbles of Nothing, 4d 𝒩 = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

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“…log y , (A. 13) where we have set an integration constant to zero without loss of generality. We recover the equivalent to (2.18), albeit with a and δ kept independent.…”

Section: A Local Dynamical Cobordisms With Curved (D − 1)-dimensional...mentioning

confidence: 99%

Section: Jhep06(2022)142 1 Introductionmentioning

confidence: 99%

At the end of the world: Local Dynamical Cobordism

Angius

Calderón-Infante

Delgado

et al. 2022

J. High Energ. Phys.

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show abstract

“…When M P → ∞, gravity is decoupled and the constraint becomes either trivially satisfied, empty of content, or violated. 10 This is consistent since swampland criteria are not meant to constrain field theories without gravity. In this section, we discuss the gravity decoupling limit in the case of the cobordism conjecture (2.14).…”

Section: Gravity Decoupling Limit Of the Cobordism Conjecturementioning

confidence: 68%

“…Therefore, the existence of a process connecting any two quantum gravity backgrounds is far from obvious too. Indeed, even if the conjecture is quite recent, already a number of works appeared studying some of its aspects and consequences, including [5][6][7][8][9][10][11]. Bordisms are relevant in several areas in mathematics and physics, a nonexhaustive list of related works is [12][13][14][15][16] for anomalies, [17,18] in relation to bubbles of nothing, [19] for the conjecture in a holographic context.…”

Section: Introductionmentioning

confidence: 99%

Looking for structure in the cobordism conjecture

Andriot¹,

Carqueville²,

Cribiori³

2022

Preprint

Self Cite

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The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza-Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.

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“…Such end-of-the-world configuration may correspond to a boundary (such as the 10d Horava-Witten boundary of 11d M-theory [2,3]), a bubble of nothing in which some compactification space shrinks to zero size [4] (see [5][6][7][8] for some recent works), or more exotic possibilities, and may possibly be dressed with charged objects, such as branes, orientifold planes or generalizations (dubbed Ifolds in [9]). The cobordism conjecture, already at this topological level, has produced interesting results, see [6,[9][10][11][12][13] for some references 2 .…”

Section: Introductionmentioning

confidence: 99%

At the End of the World: Local Dynamical Cobordism

Angius,

Calderón-Infante,

Delgado

et al. 2022

Preprint

View full text Add to dashboard Cite

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world 'branes'. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric U Sp(32) theory, Bubbles of Nothing, 4d N = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

show abstract

Open-Closed Correspondence of K-theory and Cobordism

Cited by 5 publications

References 31 publications

At the end of the world: Local Dynamical Cobordism

At the end of the world: Local Dynamical Cobordism

Looking for structure in the cobordism conjecture

At the End of the World: Local Dynamical Cobordism

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