Towards an “AdS1/CFT0” correspondence from the D(−1)/D7 system?

In this work, we investigate the existence of string theory solutions with a d-dimensional (quasi-) de Sitter spacetime, for 3 ≤ d ≤ 10. Considering classical compactifications, we derive no-go theorems valid for general d. We use them to exclude (quasi-) de Sitter solutions for d ≥ 7. In addition, such solutions are found unlikely to exist in d = 6, 5. For each no-go theorem, we further compute the d-dependent parameter c of the swampland de Sitter conjecture, $$ {M}_p\frac{\mid \nabla V\mid }{V}\ge c $$ M p ∣ ∇ V ∣ V ≥ c . Remarkably, the TCC bound $$ c\ge \frac{2}{\sqrt{\left(d-1\right)\left(d-2\right)}} $$ c ≥ 2 d − 1 d − 2 is then perfectly satisfied for d ≥ 4, with several saturation cases. However, we observe a violation of this bound in d = 3. We finally comment on related proposals in the literature, on the swampland distance conjecture and its decay rate, and on the so-called accelerated expansion bound.

“…It would correspond to a Freund-Rubin solution (see e.g. [41]), but interestingly, a pure NSNS one. Such a solution on AdS 3 × S 3 × T 4 is for instance mentioned in [42].…”

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confidence: 99%

(Quasi-) de Sitter solutions across dimensions and the TCC bound

Andriot

Horer

2023

“…In making this prediction we also assumed that the solution only has the F9 RR flux as a quantized flux, otherwise the scaling similarity would interfere with the flux quantization condition 17. Scale invariance and matrix integrals were recently explored in[40] in a related context.…”

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confidence: 99%

Scaling similarities and quasinormal modes of D0 black hole solutions

Biggs,

Maldacena

2023

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit.The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T9/5. We also present a similar argument for all other Dp-brane geometries.We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an AdS2+9/5× S8 geometry.

Instanton contributions to the ABJM free energy from quantum M2 branes

Beccaria,

Giombi,

Tseytlin

2023

We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large N and fixed level k. Using supersymmetric localization, such instanton contribution was found earlier to take the form $$ {F}^{inst}\left(N,k\right)=-{\left({\sin}^2\frac{2\pi }{k}\right)}^{-1}\exp \left(-2\pi \sqrt{\frac{2N}{k}}\right)+.\dots $$ F inst N k = − sin 2 2 π k − 1 exp − 2 π 2 N k + . … The exponent comes from the action of an M2 brane instanton wrapped on S3/ℤk, which represents the M-theory uplift of the ℂP1 instanton in type IIA string theory on AdS4 × ℂP3. The IIA string computation of the leading large k term in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor $$ {\left({\sin}^2\frac{2\pi }{k}\right)}^{-1} $$ sin 2 2 π k − 1 is reproduced by the 1-loop term in the M2 brane partition function expanded near the S3/ℤk instanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization.