$α'$-corrections and their double formulation

Lescano, Eric

doi:10.48550/arxiv.2108.12246

Cited by 3 publications

(4 citation statements)

References 40 publications

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“…This mimics an earlier observation in double field theory[13][14][15], in which the generalized gauge transformations also need to be α ′ -deformed[16][17][18][19], see also[20][21][22][23][24][25][26][27].…”

supporting

confidence: 84%

Duality invariant string beta functions at two loops

Bonezzi,

Codina,

Hohm

2021

Preprint

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We compute, for cosmological backgrounds, the O(d, d; R) invariant beta functions for the sigma model of the bosonic string at two loops. This yields an independent first-principle derivation of the order α ′ corrections to the cosmological target-space equations. To this end we revisit the quantum consistency of Tseytlin's duality invariant formulation of the worldsheet theory. While we confirm the absence of gravitational (and hence Lorentz) anomalies, our results show that the minimal subtraction scheme is not applicable, implying significant technical complications at higher loops. To circumvent these we then change gears and use the Polyakov action for cosmological backgrounds, applying a suitable perturbation scheme that, although not O(d, d; R) invariant, allows one to efficiently determine the O(d, d; R) invariant beta functions.

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confidence: 84%

Duality invariant string beta functions at two loops

Bonezzi,

Codina,

Hohm

2021

Preprint

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“…The target metric and two-form become unified into a combined object, a representative of the coset space O(n, n)/(O(n) × O(n)), known as the generalised metric, which we denote as H. The target space formulation of the dynamics of this generalised metric has been well expounded [11,12,[14][15][16][17] and has become known as Double Field Theory. 3 Starting with the seminal work of Meissner [20], there have been significant efforts [21][22][23][24][25][26] in developing the theory of higher derivative corrections in a T-duality covariant fashion (see [27] for recent lecture notes on this topic).…”

Section: Introductionmentioning

confidence: 99%

The Duality Symmetric String at Two-loops

Copland¹,

Piccinini²,

Thompson³

2021

Preprint

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The Tseytlin duality symmetric string makes manifest the O(n, n) T-duality symmetry on the worldsheet at the expense of manifest Lorentz invariance. Here we consider the two-loop renormalisation of this model in the context of "cosmological" spacetimes consisting of an internal n-dimensional torus fibred over a one-dimensional base manifold. The lack of manifest Lorentz symmetry introduces a range of complexities in momenta loop integrals which we approach using different methods. Whilst the results do satisfy a number of key consistency criteria, we find however that the two-loop counter-terms are incompatible with O(n, n) symmetry and obstruct the renormalisability of the duality symmetric string.

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“…This was in fact proven in a highly simplified scenario − called cosmological spacetime − where objects are only allowed to depend on a single coordinate. Taking it from here, there have been significant efforts [150][151][152][153][154][155] in developing the theory of higher derivative corrections in a T-duality covariant fashion (see [156] for recent lecture notes on this topic). Much more recently, the case of Poisson-Lie T-duality on group manifolds at two-loop was remarkably addressed in [157].…”

Section: Intermezzomentioning

confidence: 99%

“…The target space formulation of the dynamics of this generalised metric has been well expounded [46,85,111,112,163,164] and has become known as Double Field Theory. Starting with the seminal work of Meiss ner [149], there have been significant efforts [150][151][152][153][154][155] in developing the theory of higher derivative corrections in a T-duality covariant fashion (see [156] for recent lecture notes on this topic). This progress poses a sharp question: can one exploit worldsheet renormalisation to obtain higher derivative corrections of the target space theory in a way that maintains T-duality covariance throughout?…”

Section: Introductionmentioning

confidence: 99%

Duality and Integrability in String Theory

Piccinini¹

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This thesis investigates aspects of duality and integrable deformations in String Theory. In the first two chapters we review standard material in Mathematics and Physics, laying the ground to the novel contributions later reported. In Chapter 4 we introduce gener alised cosets, on which we are able to provide a canonical construction for a generalised frame field and spin connection that together furnish an algebra under the generalised Lie derivative. In Chapter 5 we study the geometric properties of the Yang-Baxter defor mation of CPn, showing that it constitutes an exemplar of Generalised Kähler Geometry. For CP2 we compute the generalised Kähler potential. Tangentially, we furnish a closed form for the metric and B-field of the Yang-Baxter deformed sphere Sn, for every n. In Chapter 7 we address the problem of two-loop renormalisation of the Tseytlin dou bled string for cosmological spacetimes. Whilst the results do satisfy a number of key consistency criteria, we find however that the two-loop counter-terms are incompatible with O(n, n) symmetry, pointing perhaps to the presence of scheme changes. In Chapter 8 we build on this work and set the stage for a two-loop calculation for a Poisson-Lie T-duality covariant theory.

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$α'$-corrections and their double formulation

Cited by 3 publications

References 40 publications

Duality invariant string beta functions at two loops

Duality invariant string beta functions at two loops

The Duality Symmetric String at Two-loops

Duality and Integrability in String Theory

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