The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge $q$ and mass $m$ such that $q \geq m/m_{\rm Pl}$. This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i) analyticity of light-by-light scattering, ii) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio $q/m$) and those that do not (parameterized by a coefficient $γ$). Infrared consistency implies that $q/m$ is bounded from below for small $γ$.
Cardy's conjecture about the evolution of the trace anomaly under renormalization group (RG) flows is re-interpreted as an exact, non-perturbative statement about the scaling dimension of terms in the Lagrangian of the theory. When viewed in this way, the conjecture implies that field theories which are strongly coupled in the infrared (IR) may generically host states that are not manifest as solutions to the ultraviolet (UV) complete theory's equations of motion. In particular, the scaling dimension of operators in the Hamiltonian may deviate from their classical values by $\mathcal{O}(1)$ co…
We analyze infrared consistency conditions of 3D and 4D effective field theories with massive scalars or fermions charged under multiple $U(1)$ gauge fields. At low energies, one can integrate out the massive particles and thus obtain a one-loop effective action for the gauge fields. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to-mass ratios of the massive particles from requiring that photons propagate causally and have an analytic S-matrix. We thus find that the t…
Recent studies show that there is tension between the de Sitter swampland conjectures proposed by Obeid, et al. and inflationary cosmology. In this paper, we consider an alternative to inflation, `tachyacoustic' cosmology, in light of swampland conjectures. In tachyacoustic models, primordial perturbations are generated by a period of superluminal sound speed instead of accelerating expansion. We show that realizations of tachyacoustic Lagrangians can be consistent with the de Sitter swampland conjectures, and therefore can in principle be consistent with a UV-complete theory. We derive a gene…
We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $Δϕ\lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_ϕ/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, …
A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD
d=3+1 SU（N）真空的薛定谔波泛函是在d=4中构造的配分函数;波泛函平方中的指数2S起着d=3欧几里德作用量的作用。我们开始从规范不变的猜想红外占主导地位的部分S，胶子质量M在d=4的动力学生成的基础上。我们认为，在M的逆幂展开的S中，O（M）的确切首项是d=3规范不变质量项（规范非线性西格玛模型）;下一个首项O（1/M）是传统的杨-米尔斯作用量。d=3的作用量是这两项的和，其中心涡是经典解。d=3胶子质量（我们将其限制为与M相同）和d=3耦合通过猜想与d=4耦合强度相关，但同时d=3中质量与耦合平方的无量纲比可以从d=3动力学估计。这使我们能够根据这个严格的d=3的比率来估计QCD耦合$α_s(M^2)$;我们发现一个大约为0.4的值，与早期的理论值很好地吻合，但与QCD现象学相比有点低。对于d=2+1的量子色动力学，波泛函的指数是d=2的红外有效作用量，它同时具有规范不变质量项和场强平方项，因此不同于传统的二维量子色动力学作用量，它没有质量项。这种传统的d=2的QCD将导致d=3的所有色群表示的限制。但是对于质量项（再次导致中心涡），N度= 0 mod N表示不受限制。
We revisit the cosmological dynamics of the cubic Galileon model in light of the recently proposed model-independent analyses of the Pantheon supernova data. At the background level, it is shown to be compatible with data and preferred over standard quintessence models. Furthermore, the model is shown to be consistent with the trans-Planckian censorship conjecture (as well as other Swampland conjectures). It is shown that for the given parametrization, the model fails to satisfy the bounds on the reconstructed growth index derived from the Pantheon data set at the level of linear~perturbations…
We conjecture a new sequence of dualities between Chern-Simons gauge theories simultaneously coupled to fundamental bosons and fermions. These dualities reduce to those proposed by Aharony when the number of bosons or fermions is zero. Our conjecture passes a number of consistency checks. These include the matching of global symmetries and consistency with level/rank duality in massive phases.
The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV informat…
Positivity bounds coming from consistency of UV scattering amplitudes are in general insufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL($2,\mathbb{R}$) …
We propose a scenario with string theory in the deep ultraviolet, an intermediate asymptotically safe scaling regime for gravity and matter, and the Standard Model in the infrared. This could provide a new perspective to tackle challenges of the two models: For instance, the gravitational Renormalization Group flow could connect a negative microscopic to a positive macroscopic cosmological constant, potentially rendering string theory on an anti-de Sitter background observationally viable. Further, the unitarity of a string-theoretic ultraviolet completion could be inherited by an asymptotical…
We study the thermodynamics of the Taub-NUT AdS black holes by Visser holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables $P$ and $V$, we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub-NUT black holes e.g. supercritical phase equilibrium in the $T-S$ processes, $Q-Φ$ and the Hawking-Page phase transition in the $μ-C$ processes. As a consequence, the consistency of the weak gravity conjecture of multi-char…
Infrared Consistency and the Uniqueness of String Amplitudes
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry（马克斯·普朗克研究所-台湾大学粒子物理、宇宙学与几何中心）；University of Science and Technology of China（中国科学技术大学）
We study the Weak Gravity Conjecture in the presence of scalar fields. The Weak Gravity Conjecture is a consistency condition for a theory of quantum gravity asserting that for a U(1) gauge field, there is a particle charged under this field whose mass is bounded by its charge. It was extended to a statement about any canonical pair of (p - 1)-dimensional object and p-form coupling to it, in particular to axion-instanton pairs. The gauge-scalar Weak Gravity Conjecture is a modification of this bound that includes scalar interactions. We propose a similar extension to cases where scalar fields …
The Weak Gravity Conjecture (WGC) asserts a powerful consistency condition on gauge theories coupled to gravity, and it is widely believed that its proof will shed light on the quantum origin of gravitational interactions. Holography, and in particular the AdS/CFT correspondence, is a well-suited tool by means of which it is possible to explore the world of gravity. From the holographic perspective, gravity is an emergent statistical phenomenon, and the laws of gravitation can be recast as the laws of thermodynamics. It is interesting to ask whether the WGC can be formulated in terms of the Ad…
In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form $θF \wedge F$ leads to a higher-group global symmetry between background gauge fields. At the same time, such a Chern-Simons coupling leads to a mixing between the Weak Gravity Conjectures for the axion and the gauge field, so that the charged excitations of a Weak Gravity Conjecture-satisfying axion string will also satisfy the Weak Gravity Conjecture for the gauge field. In this paper, we argue that these higher-group symmetries and this phenomenon of Weak Gravity Conjecture mixing are related to one another. We s…
We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional N=1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as $O(N^1)$ contrary to the usual $O(N^2)$ scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS …
