JHEP09(2021)036 Springer August 4, 2021 August 16, 2021 January 4, 2021 : : : September 7, 2021 : Revised Received -branes Accepted p Published Published for SISSA by https://doi.org/10.1007/JHEP09(2021)036 . 3 2011.11868 The Authors. c Global Symmetries, Black Holes in String Theory,

We discuss a topological reason why global symmetries are not conserved in , [email protected] Department of , Tohoku University, Sendai 980-8578, Japan E-mail: -form gauge field. Our topological construction is motivated by the brane/black-brane Open Access Article funded by SCOAP Keywords: ArXiv ePrint: the shift symmetry ofp an axion-like field whichcorrespondence, originates brane from instantons, and themay an compactification be idea of realized that a by virtual surgery black on branes manifolds. of a simple kind Abstract: quantum , at leastform when symmetry. the The symmetrybreaking mechanism comes term is from in purely compactification the topologicalcharge of UV conservation and in Lagrangian. a does a higher not sum Local require over current geometries any conservation in explicit does the not path imply integral. global We explicitly consider Kazuya Yonekura gravity Topological violation of global symmetries in quantum JHEP09(2021)036 ] ]. ].) 12 13 10 20 17 , 16 ]. Such 4 ]. (See also [ , 3 -form symmetries [ 15 p – 13 ]). For example, the problem 4 , 4 3 9 5 6 -parameters [ – 1 – α 0 4 = 0 p > p ]. 2 ] which all indicate that Euclidean wormholes are important 19 , 18 12 -form global symmetry , p ] (or Coleman’s 11 10 ] for other discussions.) We argue that the relevant geometries for the 1 10 12 22 , -form symmetries are obtained by surgery on Euclidean spacetime (and its p 21 , 9 ]). One of the arguments is based on Euclidean wormholes [ 9 – 1 In this paper, we study the problem in a broader context of However, there are still some mysteries, such as how to interpret the appearance of There are some conceptual difficulties in the interpretation of the results based on 5.2 Speculations on the case 4.3 Topological obstruction4.4 to charge conservation Example 5.1 Brief summary of the case 4.1 The theory4.2 and Brane instanton and spacetime surgery (See also [ violation of generalization which we leave toin future work). in We later will sections. explain Euclidean surgery wormholes are and special its cases motivation of more general ingredients of quantum gravity. These developments,into as violation well of as global others, symmetries lead in to quantum new gravity, insights see e.g.ensemble [ of theories [ can be sharpened byhave considering a Euclidean definite wormholes CFT in dual AdS [ spaces which are known to Euclidean wormholes, such asand the ensemble fact of theories that (or thoseIt in wormholes other was may words not random require couplings) soRecently baby rather universes clear there than a whether are single weand several theory. replica should developments wormholes include such [ them as in exact the solutions gravitational of path the integral. JT gravity [ There is strong evidence(e.g. [ that exact globalmay symmetries induce terms do in not the exist low energy in effective quantum theory gravity which violate global symmetries. 1 Introduction 5 Discussions 3 Virtual black branes as4 surgery Violation of shift symmetry of axion-like fields Contents 1 Introduction 2 The general mechanism JHEP09(2021)036 - p (2.1) (2.2) (2.3) -form ]. There 25 – + 1) p 23 ( and the final global symme- are qualitatively , we have −∞ is the (Euclidean) 0 Σ = U(1) R ], but we will not discuss 2 × t ]. ] p > , and define the charge 27 which is a , 20 ∞ Y 26 J + -form . ⊂ , p Y , where Σ Y × −∞ × R . -form symmetries by more general R ⊂ Γ p Γ = [ ∂ = Σ ?J, = X , Σ ] appeared which also discusses global symmetry -