Deformed $$\sigma $$-models, Ricci flow and Toda field theories

Bykov, Dmitri; Lüst, Dieter

doi:10.1007/s11005-021-01484-0

Cited by 8 publications

(13 citation statements)

References 93 publications

(153 reference statements)

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“…which precisely reduces to the behaviour discussed in [11] in the case of AdS, and generalisations thereof. This way, exploiting mathematical methods which are rooted in string theory via the σ-model graviton renormalisation group flow, the Swampland distance conjecture for the metric was rephrased and specified as the Ricci flow conjecture [16][17][18][19]. The reader is strongly suggested to refer to [20][21][22][23][24][25] for comprehensive discussions of the techniques that are usually employed when studying Ricci flow of differentiable manifolds.…”

Section: Jhep01(2023)126mentioning

confidence: 99%

Cobordism, singularities and the Ricci flow conjecture

Velázquez

Biasio

Lüst

2023

J. High Energ. Phys.

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In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented. This is done by starting from a suitable manifold with trivial cobordism class, applying surgery techniques to Ricci flow singularities and trivialising the cobordism class of one of the resulting connected components via the introduction of appropriate defects. The specific example of $$ {\varOmega}_4^{SO} $$ Ω 4 SO is studied in detail. A connection between the process of blowing up a point of a manifold and that of taking the connected sum of such with ℂℙn is explored. Hence, the problem of studying the Ricci flow of a K3 whose cobordism class is trivialised by the addition of 16 copies of ℂℙ2 is tackled by applying both the techniques developed in the previous sections and the classification of singularities in terms of ADE groups.

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Section: Jhep01(2023)126mentioning

confidence: 99%

Cobordism, singularities and the Ricci flow conjecture

Velázquez

Biasio

Lüst

2023

J. High Energ. Phys.

Self Cite

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“…which allows us to rewrite the expected metric as follows: and dropping the primes, we can finally rewrite the metric of our unknown space g(w) as the so-called "Sausage metric" [18,19] with parameter t as introduced by Lambert et al:…”

Section: T T Deformation On Adsmentioning

confidence: 99%

$T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory

2022

Preprint

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In this paper, we shed new light onto T T -deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between T T -deformations, gravity and Chern-Simons theory and suggests that the formalism developed in this paper and the gravity picture of T T -deformations should be closely related.

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“…and dropping the primes, we can finally rewrite the metric of our unknown space g(w) as the so-called "Sausage metric" [20,21] with parameter t as introduced in [21]:…”

Section: Jhep08(2022)101mentioning

confidence: 99%

$$ T\overline{T} $$ deformations in curved space from 4D Chern-Simons theory

2022

J. High Energ. Phys.

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In this paper, we shed new light onto $$ T\overline{T} $$ T T ¯ -deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT’s, in a 4D Chern-Simons bulk. This approach is motivated by various connections between $$ T\overline{T} $$ T T ¯ -deformations, gravity and Chern-Simons theory and suggests that the formalism developed in this paper and the gravity picture of $$ T\overline{T} $$ T T ¯ -deformations should be closely related.

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Deformed $$\sigma $$-models, Ricci flow and Toda field theories

Abstract: It is shown that the Pohlmeyer map of a $$\sigma $$ σ -model with a toric two-dimensional target space naturally leads to the ‘sausage’ metric. We then elaborate the trigonometric deformation of the $$\mathbb {CP}^{n-1}$$ CP n - 1 -model, proving that its… Show more

Cited by 8 publications

References 93 publications

Cobordism, singularities and the Ricci flow conjecture

Cobordism, singularities and the Ricci flow conjecture

$T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory

$$ T\overline{T} $$ deformations in curved space from 4D Chern-Simons theory

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