arXiv subjects

Joel Karlsson

Publications and source records attributed to Joel Karlsson.

8 recordsLinked to original sources

arXiv2026

Quantum Liouville Cosmology

We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators, taken along a judiciously chosen complex contour, yield states akin to the Hartle-Hawking wavefunction. Working in the fixed $K$-representation, where $K$ is the trace of the extrinsic curvature, we compute the one-loop wavefunctions and put forward a conjecture for the all-loop expressions. A suitable pairing of Liouville disk path integrals yields a $K$-independent quantity that may form the basis for a well-defined inner product on the space of Euclidean histories. We also consider other ensembles, including one with fixed area, and provide a static patch perspective with a timelike feature.

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arXiv2026

The IKKT renormalization group flow is IIB: toward zero-d holography

Supergravity solutions describing stacks of D$p$-branes with $p\neq 3$ feature a non-constant dilaton profile, which is holographically mapped to the running of the SYM coupling in $(p+1)$ dimensions. For D-instantons ($p=-1$), the lack of space and time in the IKKT matrix model makes such an interpretation difficult at first. In this letter, we propose a method to achieve this based on two closely related concepts: the IKKT method of integrating out heavy strings in a Coulomb branch vacuum and the matrix RG flow of Brézin and Zinn-Justin (BZJ). The notable difference between the two is that the BZJ RG flow also integrates over the Coulomb branch position. We first apply the Coulomb branch method and by relating the coefficient of the leading correction to the IKKT action with the string coupling, we can compute its dependence on the Coulomb branch position, finding a match between matrix theory and supergravity. Next, we apply the BZJ-flow to the IKKT partition function, which leads to a running of the coupling constant $g$ with the rank $N$ of the matrix model, reproducing the $N$-dependence of the axio-dilaton field in supergravity.

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arXiv2026

An ode to instantons

We present a formalism for semiclassical time evolution in quantum mechanics, building on a century of work. We identify complex saddle points in real time, real saddle points in complex time, and complex saddle points in complex time that reproduce the known answers in classic problems. For the decay of a metastable state, we find finite time and finite energy analogs of the "bounce" which do not have strict zero or negative modes. The one-loop phase of the wave function and the multiplicity of bounce solutions at late times are discussed. The motivation of this work is to learn how to compute decay rates in quantum field theory in situations with non-trivial time dependence, by first taking a humble step backwards to the fascinating world of quantum mechanics.

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arXiv2024

The Kontsevich-Segal Criterion in the No-Boundary State Constrains Anisotropy

We show that the Kontsevich-Segal-Witten (KSW) criterion applied to the no-boundary state constrains anisotropic deformations of de Sitter space. We consider squashed $S^3$ and $S^1 \times S^2$ boundaries and find that in both models, the KSW criterion excludes a significant range of homogeneous but anisotropic configurations. For squashed $S^3$ boundaries, the excluded range includes all surface geometries with negative scalar curvature, in line with dS/CFT reasoning. For $S^1 \times S^2$ boundaries, we find that KSW selects the low-temperature regime of configuration space where the $S^1$ is sufficiently large compared to the $S^2$. In both models, the KSW criterion renders the semiclassical wave function normalizable, up to one-loop effects.

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arXiv2024

The complete Kaluza-Klein spectra of $\mathcal{N} = 1$ and $\mathcal{N} = 0$ M-theory on $AdS_4 \times (\text{squashed } S^7)$

The squashed seven-sphere operator spectrum is completed by deriving the spectrum of the spin-3/2 operator. The implications of the results for the $AdS_4$ $\mathcal{N} = 1$ supermultiplets obtained from compactification of eleven-dimensional supergravity are analysed. The weak $G_2$ holonomy plays an important role when solving the eigenvalue equations on the squashed sphere. Here, a novel and more universal algebraic approach to the whole eigenvalue problem on coset manifolds is provided. Having obtained full control of all the operator spectra, we can finally determine the irreps $D(E_0, s)$ for all supermultiplets in the left-squashed vacuum. This includes an analysis of possible boundary conditions. By performing an orientation flip on the seven-sphere, we also obtain the full spectrum for the non-supersymmetric right-squashed compactification which is of interest in the swampland context and in particular for the $AdS$ swampland conjecture. Here, a number of boundary condition ambiguities arise making the analysis of dual marginal operators somewhat involved. This work is a direct continuation of [1] and [2].

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arXiv2024

Microscopics of de Sitter Entropy from Precision Holography

We calculate quantum corrections to the entropy of four-dimensional de Sitter space induced by higher-derivative terms in the gravitational action and by one-loop effects. Employing the intertwinement in semiclassical gravity of Euclidean de Sitter and anti-de Sitter saddles, we embed effective de Sitter gravity theories in M-theory and express the entropy in terms of the regularized Euclidean anti-de Sitter action on an auxiliary $\mathrm{EAdS}_4 \times S^7/\mathbb{Z}_k$ background. We conjecture that the partition function of the holographically dual 3d ABJM CFT determines the explicit form of the corrections to the de Sitter entropy. This includes a logarithmic term, the coefficient of which, we show, agrees with an independent one-loop calculation around the $-S^4 \times S^7/\mathbb{Z}_k$ Euclidean de Sitter saddle. This provides evidence that the microscopic degrees of freedom behind the entropy of four-dimensional de Sitter space in gravitational theories with a holographic dual description are encapsulated by the path integral of the Euclidean CFT on the three-sphere.

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arXiv2023

The Kontsevich-Segal Criterion in the No-Boundary State Constrains Inflation

We show that the Kontsevich-Segal (KS) criterion, applied to the complex saddles that specify the semiclassical no-boundary wave function, acts as a selection mechanism on inflationary scalar field potentials. Completing the observable phase of slow-roll inflation with a no-boundary origin, the KS criterion effectively bounds the tensor-to-scalar ratio of cosmic microwave background fluctuations to be less than 0.08, in line with current observations. We trace the failure of complex saddles to meet the KS criterion to the development of a tachyon in their spectrum of perturbations.

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arXiv2021

Compactifications of String/M-Theory and the Swampland: A Study of the AdS$_\text{4}$ Mass Spectrum of Eleven-Dimensional Supergravity on the Squashed Seven-Sphere

The landscape of possible four-dimensional low-energy effective theories arising from compactifications of string/M-theory seems vast. This might lead one to believe that any consistent-looking effective field theory coupled to gravity can be obtained as a low-energy limit of string theory. However, a set of "swampland" conjectures suggests that this is not true and that, in fact, there is an even larger set of effective field theories that cannot be obtained in this way. In particular, the AdS instability swampland conjecture asserts that nonsupersymmetric anti-de Sitter vacua are unstable. These swampland criteria can have implications for, for instance, low-energy physics and cosmology. M-theory is a nonperturbative unification of all superstring theories. Its low-energy limit, eleven-dimensional supergravity, admits two compactifications on the squashed seven-sphere. One of the solutions has one unbroken supersymmetry ($\mathcal{N} = 1$) while the other has none ($\mathcal{N} = 0$). Due to the AdS instability swampland conjecture, the latter should be unstable. However, this has not been demonstrated explicitly. To study the stability of the $\mathcal{N} = 0$ vacuum, we investigate the mass spectrum of the theory. The main advancement compared to previous attempts is the realisation that all mass operators in the Freund-Rubin compactification are related to a universal Laplacian, allowing us to relate Weyl tensor terms to group invariants. One limitation of the group-theoretical method we employ is that it can lead to false roots. This is remedied, at least in part, by demanding that the fields form supermultiplets in the $\mathcal{N} = 1$ case. Although we arrive at an eigenvalue spectrum for all operators of interest, there is a hint that the results may be incomplete. Thus, we do not reach a decisive conclusion regarding the investigated type of instability.

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