Instanton Action Research Articles

Seeded vacuum decay with Gauss-Bonnet

We investigate false vacuum decay catalysed by black holes under the influence of the higher order Gauss-Bonnet term. We study both bubble nucleation and Hawking-Moss types of phase transition in arbitrary dimension. The equations of motion of “bounce” solutions in which bubbles nucleate around arbitrary dimensional black holes are found in the thin wall approximation, and the instanton action is computed. The headline result that the tunnelling action for static instantons is the difference in entropy of the seed and remnant black holes is shown to hold for arbitrary dimension. We also study the Hawking-Moss transition and find a picture similar to the Einstein case, with one curious five-dimensional exception (due to a mass gap). In four dimensions, we find as expected that the Gauss-Bonnet term only impacts topology changing transitions, i.e. when vacuum decay removes the seed black hole altogether, or in a (Hawking-Moss) transition where a black hole is created. In the former case, topology changing transitions are suppressed (for positive GB coupling α), whereas the latter case results in an enhanced transition.

The power of Lorentzian wormholes

As shown by Louko and Sorkin in 1995, topology change in Lorentzian signature involves spacetimes with singular points, which they called crotches. We modify their construction to obtain Lorentzian semiclassical wormholes in asymptotically AdS. These solutions are obtained by inserting crotches on known saddles, like the double-cone or multiple copies of the Lorentzian black hole. The crotches implement swap-identifications, and are classically located near an extremal surface. The resulting Lorentzian wormholes have an instanton action equal to their area, which is responsible for topological suppression in any number of dimensions.We conjecture that including such Lorentzian wormhole spacetimes is equivalent to path integrating over all mostly Euclidean smooth spacetimes. We present evidence for this by reproducing semiclassical features of the genus expansion of the spectral form factor, and of a late-time two point function, by summing over the moduli space of Lorentzian wormholes. As a final piece of evidence, we discuss the Lorentzian version of West-Coast replica wormholes.

PQ axiverse

We show that the strong CP problem is solved in a large class of compactifications of string theory. The Peccei-Quinn mechanism solves the strong CP problem if the CP-breaking effects of the ultraviolet completion of gravity and of QCD are small compared to the CP-preserving axion potential generated by low-energy QCD instantons. We characterize both classes of effects. To understand quantum gravitational effects, we consider an ensemble of flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces in the geometric regime, taking a simple model of QCD on D7-branes. We show that the D-brane instanton contribution to the neutron electric dipole moment falls exponentially in N4, with N the number of axions. In particular, this contribution is negligible in all models in our ensemble with N > 17. We interpret this result as a consequence of large N effects in the geometry that create hierarchies in instanton actions and also suppress the ultraviolet cutoff. We also compute the CP breaking due to high-energy instantons in QCD. In the absence of vectorlike pairs, we find contributions to the neutron electric dipole moment that are not excluded, but that could be accessible to future experiments if the scale of supersymmetry breaking is sufficiently low. The existence of vectorlike pairs can lead to a larger dipole moment. Finally, we show that a significant fraction of models are allowed by standard cosmological and astrophysical constraints.

Axionic Festina Lente

The swampland conjecture known as Festina Lente (FL) imposes a lower bound on the mass of all charged particles in a quasi-de Sitter space. In this paper, we propose the aFL (axionic Festina Lente) bound, an extension of FL to axion-like particles arising from type II string theory. We find that the product of the instanton action and the axion decay constant is bounded from below by the vacuum energy. This is achieved indirectly, using dimensional reduction on Calabi-Yau threefolds, and translating the FL result for dipoles into a purely geometric bound. We discuss axionic black holes evolution, and aFL constraints on Euclidean wormholes, showing that the gravitational arguments leading to the FL bound for U(1) charged particles cannot be directly applied to axions. Moreover, we discuss phenomenological implications of the aFL bound, including constraints on string inflation models and the axion-photon coupling via kinetic mixing.

Instanton expansions and phase transitions

A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potential’s instanton expansion. We argue, using the Yang-Lee theory of phase transitions, that the theory breaks down in the classic sense: states become light. However, these states are not necessarily light for all values of the axion and there can be large regions where the effective description remains valid. We find alternative expressions for the effective potential in terms of the properties of these light states, which remain useful even when the instanton expansion breaks down, and thus initiate a push beyond the lamppost of large instanton actions. Most of these questions are motivated by the axionic Weak Gravity Conjecture, which we reformulate without reference to instanton actions. We also comment on its ability to constrain large-field axion inflation.

Fuzzy Dark Matter candidates from string theory

String theory has been claimed to give rise to natural fuzzy dark matter candidates in the form of ultralight axions. In this paper we revisit this claim by a detailed study of how moduli stabilisation affects the masses and decay constants of different axion fields which arise in type IIB flux compactifications. We find that obtaining a considerable contribution to the observed dark matter abundance without tuning the axion initial misalignment angle is not a generic feature of 4D string models since it requires a mild violation of the Sf ≲ MP bound, where S is the instanton action and f the axion decay constant. Our analysis singles out C4-axions, C2-axions and thraxions as the best candidates to realise fuzzy dark matter in string theory. For all these ultralight axions we provide predictions which can be confronted with present and forthcoming observations.

Emptiness formation in polytropic quantum liquids

We study large deviations in interacting quantum liquids with the polytropic equation of state P(ρ) ∼ ρ γ , where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ⩾ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

Black hole pair production on cosmic strings in the presence of a background magnetic field

We investigate the pair creation of magnetically charged black holes on a cosmic string in the presence of a background magnetic field. The string may either break or fray to produce a pair of accelerating black holes described by Ernst metric. By using the instanton action we obtain the rate of such production. For large values of background magnetic field the production of large black holes is probable. Comparing our results with the case of black hole pair creation in magnetic field with no string, we show that fraying/breaking of the cosmic string can substantially enhance the production rate. We also obtain the result of monopole-antimonopole pair production on cosmic string in an external magnetic field, using the WKB approximation and compare it with the black hole results. We also provide a heuristic study of black hole pair creation on cosmic string in the presence of a magnetic field in the de Sitter background, although the analog of Ernst metric with a cosmological constant is lacking. Like a cosmic string and/or a background magnetic field, a positive cosmological constant increases the production rate.

Higgs vacuum decay in a braneworld

We examine the effect of large extra dimensions on vacuum decay in the Randall–Sundrum (RS) braneworld paradigm. We assume the scalar field is confined to the brane, and compute the probability for forming an “anti-de Sitter” (AdS) bubble inside a critical flat RS brane. We present the first full numerical solutions for the brane instanton considering two test potentials for the scalar field. We explore the geometrical impact of thin and thick bubble walls, and compute the instanton action in a range of cases. We conclude by commenting on a more physically realistic potential relevant for the Standard Model Higgs. For bubbles with large backreaction, the extra dimension has a dramatic effect on the tunnelling rate, however, for the weakly backreacting bubbles more relevant for realistic Standard Model potentials, the extra dimension has little impact.

Brown-Teitelboim instantons and thermodynamics of de Sitter and anti–de Sitter space

We study the instantons (or bounces) in the Brown-Teitelboim (BT) mechanism of relaxation of cosmological constant which is a cosmological version of the Schwinger mechanism. The BT mechanism is a false vacuum decay of (A)dS$_{d+1}$ (and $R^{1, d}$) spaces via spontaneous nucleations of spherical $(d-1)$-branes and thus ostensibly has bearings on (A)dS$_{d+1}$/CFT$_d$ holography. In this paper we focus on the four-dimensional case, although the higher or lower-dimensional generalization is straightforward. As is the case with pair productions near black hole and de Sitter horizons, we show that the BT instanton action for a membrane nucleation encodes the first law of thermodynamics of (Anti) de Sitter space. In particular, the membrane instanton precisely accounts for the change of entropy of (A)dS space before and after nucleation, in good accordance with AdS$_{d+1}$/CFT$_d$ in which the $(d-1)$-branes make up all degrees of freedom of AdS$_{d+1}$ space. In light of this lesser-known perspective presented here we also make remarks on (1) (A)dS/CFT and (2) complexity. For the complexity we observe that the Lorentzian bounce action may have close connection to complexity.

Instantons via breaking geometric symmetry in hyperbolic traps

Using geometrical and algebraic ideas, we study tunnel eigenvalue asymptotics and tunnel bilocalization of eigenstates for certain class of operators (quantum Hamiltonians) including the case of Penning traps, well known in physical literature. For general hyperbolic traps with geometric asymmetry, we study resonance regimes which produce hyperbolic type algebras of integrals of motion. Such algebras have polynomial (non-Lie) commutation relations with creation-annihilation structure. Over this algebra, the trap asymmetry (higher-order anharmonic terms near the equilibrium) determines a pendulum-like Hamiltonian in action-angle coordinates. The symmetry breaking term generates a tunneling pseudoparticle (closed instanton). We study the instanton action and the corresponding spectral splitting.

One-loop Pfaffians and large-field inflation in string theory

We study the consistency of large-field inflation in low-energy effective field theories of string theory. In particular, we focus on the stability of Kähler moduli in the particularly interesting case where the non-perturbative superpotential of the Kähler sector explicitly depends on the inflaton field. This situation arises generically due to one-loop corrections to the instanton action. The field dependence of the modulus potential feeds back into the inflationary dynamics, potentially impairing slow roll. We distinguish between world-sheet instantons from Euclidean D-branes, which typically yield polynomial one-loop Pfaffians, and gaugino condensates, which can yield exponential or periodic corrections. In all scenarios successful slow-roll inflation imposes bounds on the magnitude of the one-loop correction, corresponding to constraints on possible compactifications. While we put a certain emphasis on Type IIB constructions with mobile D7-branes, our results seem to apply more generally.

Universality of the topological string at large radius and NS-brane resurgence

We show that there is a natural universal limit of the topological string free energies at the large radius point. The new free energies keep a nonholomorphic dependence on the complex structure moduli space and their functional form is the same for all Calabi-Yau geometries, compact and noncompact alike. The asymptotic nature of the free energy expansion changes in this limit due to a milder factorial growth of its coefficients, and this implies a transseries extension with instanton effects in $\exp(- 1/g_s^2)$, of NS-brane type, rather than $\exp(-1/g_s)$, of D-brane type. We show a relation between the instanton action of NS-brane type and the volume of the Calabi-Yau manifold which points to a possible interpretation in terms of NS5-branes. A similar rescaling limit has been considered recently leading to an Airy equation for the partition function which is here used to explain the resurgent properties of the rescaled transseries.

Complex saddle points in the Gross-Witten-Wadia matrix model

We give an exhaustive characterization of the complex saddle point configurations of the Gross-Witten-Wadia matrix model in the large-N limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, in terms of the values of the coupling constant and of the fraction of the total unit density that is supported in one of the arcs, and derive an explicit condition for gap closing associated to nonvacuum saddles. By applying the idea of large-N instanton we also give direct analytic derivations of the weak-coupling and strong-coupling instanton actions.

Sharpening the weak gravity conjecture with dimensional reduction

We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a "Lattice Weak Gravity Conjecture" that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.

Planckian axions and the Weak Gravity Conjecture

Several recent works have claimed that the Weak Gravity Conjecture (WGC) excludes super-Planckian displacements of axion fields, and hence large-field axion inflation, in the absence of monodromy. We argue that in theories with $N\gg1$ axions, super-Planckian axion diameters $\cal{D}$ are readily allowed by the WGC. We clarify the nontrivial relationship between the kinetic matrix $K$ --- unambiguously defined by its form in a Minkowski-reduced basis --- and the diameter of the axion fundamental domain, emphasizing that in general the diameter is not solely determined by the eigenvalues $f_1^2 \le ... \le f_N^2$ of $K$: the orientations of the eigenvectors with respect to the identifications imposed by instantons must be incorporated. In particular, even if one were to impose the condition $f_N<M_{pl}$, this would imply neither ${\cal D}<M_{pl}$ nor ${\cal D}<\sqrt{N}M_{pl}$. We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by $S \ge {\cal S} M_{pl}/f_N$, with ${\cal S}$ a fixed constant, but in the universal limit $S\gtrsim {\cal S} \sqrt{N}M_{pl}/f_N$. Thus, having $f_N>M_{pl}$ does not immediately imply the existence of unsuppressed higher harmonic contributions to the potential. Finally, we argue that in effective axion-gravity theories, the zero-form version of the WGC can be satisfied by gravitational instantons that make negligible contributions to the potential.

Quantum decay of the supercurrent and intrinsic capacitance of Josephson junctions beyond the tunnel limit

A nondissipative supercurrent state of a Josephson junction is metastable with respect to the formation of a finite-resistance state. This transition is driven by fluctuations, thermal at high temperatures and quantum at low temperatures. We evaluate the lifetime of such a state due to quantum fluctuations in the limit when the supercurrent is approaching the critical current. The decay probability is determined by the instanton action for the superconducting phase difference across the junction. At low temperatures, the dynamics of the phase is massive and is determined by the effective capacitance, which is a sum of the geometric and intrinsic capacitance of the junction. We model the central part of the Josephson junction either by an arbitrary short mesoscopic conductor described by the set of its transmission coefficients, or by a diffusive wire of an arbitrary length. The intrinsic capacitance can generally be estimated as ${C}_{*}\ensuremath{\sim}G/{E}_{g}$, where $G$ is the normal-state conductance of the junction and ${E}_{g}$ is the proximity minigap in its normal part. The obtained capacitance is sufficiently large to qualitatively explain the hysteretic behavior of the current-voltage characteristic even in the absence of overheating.

Hydrodynamics, resurgence, and transasymptotics

The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions.

Fencing in the swampland: quantum gravity constraints on large field inflation

In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T- duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. We argue that, if the strong version is violated, the constraints on large field inflation can be evaded while still satisfying the mild one. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local $${\mathbb{C}\mathbb{P}^2}$$ C P 2

The holomorphic anomaly equations describe B-model closed topological strings in Calabi–Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local $${\mathbb{C}\mathbb{P}^2}$$ toric Calabi–Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors. In particular, analyzing the asymptotic growth of the perturbative free energies, one finds contributions from three different instanton actions related by $${\mathbb{Z}_3}$$ symmetry, alongside another action related to the Kähler parameter. Resurgent transseries methods then compute, from the extended holomorphic anomaly equations, higher instanton sectors and it is shown that these precisely control the asymptotic behavior of the perturbative free energies, as dictated by resurgence. The asymptotic large-order growth of the one-instanton sector unveils the presence of resonance, i.e., each instanton action is necessarily joined by its symmetric contribution. The structure of different resurgence relations is extensively checked at the numerical level, both in the holomorphic limit and in the general nonholomorphic case, always showing excellent agreement with transseries data computed out of the nonperturbative holomorphic anomaly equations. The resurgence relations further imply that the string free energy displays an intricate multi-branched Borel structure, and that resonance must be properly taken into account in order to describe the full transseries solution.