IA Scholar Query: Effective categoricity of Abelian p-groups.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 22 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Integral Arnol'd Conjecture
https://scholar.archive.org/work/3smnpo3fejhgveuhtc6r422ilu
We explain how to adapt the methods of Abouzaid-McLean-Smith to the setting of Hamiltonian Floer theory. We develop a language around equivariant "⟨ k ⟩-manifolds", which are a type of manifold-with-corners that suffices to capture the combinatorics of Floer-theoretic constructions. We describe some geometry which allows us to straightforwardly adapt Lashofs's stable equivariant smoothing theory and Bau-Xu's theory of FOP-perturbations to ⟨ k ⟩-manifolds. This allows us to compatibly smooth global Kuranishi charts on all Hamiltonian Floer trajectories at once, in order to extract a Floer complex and prove the Arnol'd conjecture over the integers. We also make first steps towards a further development of the theory, outlining the analog of bifurcation analysis in this setting, which can give short independence proofs of the independence of Floer-theoretic invariants of all choices involved in their construction.Semon Rezchikovwork_3smnpo3fejhgveuhtc6r422iluThu, 22 Sep 2022 00:00:00 GMTAdaptive syndrome measurements for Shor-style error correction
https://scholar.archive.org/work/55di3m5yjvdwbklalsbqpura3e
The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates and ancilla qubits prepared in the cat state in syndrome extraction circuits to prevent propagation of errors caused by gate faults. For a stabilizer code that can correct up to t errors, the traditional Shor scheme handles ancilla preparation and measurement faults by performing syndrome measurements until the syndromes are repeated t+1 times in a row; in the worst-case scenario, (t+1)^2 rounds of measurements are required. In this work, we improve the Shor FTEC scheme using an adaptive syndrome measurement technique. In particular, our protocols determine a syndrome for error correction based on information from the differences of syndromes obtained from any two consecutive rounds. Our protocol that satisfies the strong FTEC conditions requires no more than (t+3)^2/4-1 rounds of measurements and is applicable to any stabilizer code. Compared to the traditional method, we estimate that our adaptive measurement method could increase the fault-tolerant threshold by a factor of 4 in the large t limit. We also extend our ideas to error correction satisfying the weak FTEC conditions and flag FTEC.Theerapat Tansuwannont, Kenneth R. Brownwork_55di3m5yjvdwbklalsbqpura3eThu, 22 Sep 2022 00:00:00 GMTTame parahoric nonabelian Hodge correspondence on curves
https://scholar.archive.org/work/upwtjfbvcjf57jz74jslk7zeci
The nonabelian Hodge correspondence for vector bundles over noncompact curves is adequately described by implementing a weighted filtration on the objects involved. In order to establish a full correspondence between a Dolbeault and a de Rham space for a general complex reductive group G, we introduce torsors given by parahoric group schemes in the sense of Bruhat–Tits. Combined with existing results on the Riemann–Hilbert correspondence for logarithmic parahoric connections, this gives a full nonabelian Hodge correspondence from Higgs bundles to fundamental group representations over a noncompact curve beyond the GL_n(ℂ)-case.Pengfei Huang, Georgios Kydonakis, Hao Sun, Lutian Zhaowork_upwtjfbvcjf57jz74jslk7zeciThu, 22 Sep 2022 00:00:00 GMTThe Branes Behind Generalized Symmetry Operators
https://scholar.archive.org/work/yaux262fkfavvkigxfiwkyzoxy
The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d-m-1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary ∂ X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in ∂ X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.Jonathan J. Heckman, Max Hübner, Ethan Torres, Hao Y. Zhangwork_yaux262fkfavvkigxfiwkyzoxyThu, 22 Sep 2022 00:00:00 GMTHamiltonian facets of classical gauge theories on E-manifolds
https://scholar.archive.org/work/ac3ikarjujczfj3tgmcv7y5f6u
Manifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in [NT01] and investigated in depth in [MS20]. In this article we explore their physical facets by extending gauge theories to the E-category. Singularities in the configuration space of a classical particle can be described in several new scenarios unveiling their Hamiltonian aspects on an E-symplectic manifold. Following the scheme inaugurated in [Wei78], we show the existence of a universal model for a particle interacting with an E-gauge field. In addition, we generalize the description of phase spaces in Yang-Mills theory as Poisson manifolds and their minimal coupling procedure, as shown in [Mon86], for base manifolds endowed with an E-structure. In particular, the reduction at coadjoint orbits and the shifting trick are extended to this framework. We show that Wong's equations, which describe the interaction of a particle with a Yang-Mills field, become Hamiltonian in the E-setting. We formulate the electromagnetic gauge in a Minkowski space relating it to the proper time foliation and we see that our main theorem describes the minimal coupling in physical models such as the compactified black hole.Pau Mir, Eva Miranda, Pablo Nicoláswork_ac3ikarjujczfj3tgmcv7y5f6uWed, 21 Sep 2022 00:00:00 GMTVertex operator algebra and colored parenthesized braid operad
https://scholar.archive.org/work/sk7zhpxprzejhoenowrqvit7yq
The colored parenthesized braid operad is a sequence of full subcategories of the fundamental groupoids of the configuration spaces of the complex plane, and a conformal block, a physical quantity of chiral two-dimensional conformal field theory, is a sheaf on the configuration space, which is mathematically formulated in terms of a vertex operator algebra and its modules. In this paper we show that the colored parenthesized braid operad acts weakly 2-categorically on a module category of a vertex operator algebra whose object is a module M such that M and M^∨ are C_1-cofinite. If this action induces a 1-categorical action, then the module category inherits a balanced braided tensor category structure, which is shown for a rational C_2-cofinite vertex operator algebra. This gives an alternative proof of a result of Huang and Lepowsky.Yuto Moriwakiwork_sk7zhpxprzejhoenowrqvit7yqWed, 21 Sep 2022 00:00:00 GMTCategorical symmetries of T-duality
https://scholar.archive.org/work/tj3r2qqgxbcydejwpp7kielrva
Topological T-duality correspondences are higher categorical objects that can be classified by a strict Lie 2-group. In this article we compute the categorical automorphism group of this 2-group; hence, the higher-categorical symmetries of topological T-duality. We prove that the categorical automorphism group is a non-central categorical extension of the integral split pseudo-orthogonal group. We show that it splits over several subgroups, and that its k-invariant is 2-torsion.Konrad Waldorfwork_tj3r2qqgxbcydejwpp7kielrvaWed, 21 Sep 2022 00:00:00 GMTMultiplicities and dimensions in enveloping tensor categories
https://scholar.archive.org/work/rnrls3wbmfgmdnj2tz52b2auam
In the previous paper arxiv:math/0610552 semisimple tensor categories were constructed out of certain regular Mal'cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple objects. This yields also the Grothendieck ring. The main tool is the subquotient decomposition of the basic objects.Friedrich Knopwork_rnrls3wbmfgmdnj2tz52b2auamWed, 21 Sep 2022 00:00:00 GMTCancellation theorems for reciprocity sheaves
https://scholar.archive.org/work/tsnbrr7lezhndbmxyt6pqlybsy
We prove cancellation theorems for reciprocity sheaves and cube-invariant modulus sheaves with transfers of Kahn–Saito–Yamazaki, generalizing Voevodsky's cancellation theorem for 𝐀^1-invariant sheaves with transfers. As an application, we get some new formulas for internal hom's of the sheaves Ω^i of absolute Kähler differentials.Alberto Merici, Shuji Saitowork_tsnbrr7lezhndbmxyt6pqlybsyTue, 20 Sep 2022 00:00:00 GMTLogarithmic Donaldson-Thomas theory
https://scholar.archive.org/work/6jbggtflrzgrjj224fibwhnqde
Let X be a smooth threefold with a simple normal crossings divisor D. We construct the Donaldson-Thomas theory of the pair (X|D) enumerating ideal sheaves on X relative to D. These moduli spaces are compactified by studying subschemes in expansions of the target geometry, and the moduli space carries a virtual fundamental class leading to numerical invariants with expected properties. We formulate punctual evaluation, rationality and wall-crossing conjectures, in parallel with the standard theory. Our formalism specializes to the Li-Wu theory of relative ideal sheaves when the divisor is smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with expansions.Davesh Maulik, Dhruv Ranganathanwork_6jbggtflrzgrjj224fibwhnqdeTue, 20 Sep 2022 00:00:00 GMTOPE-based Methods in Nonperturbative QCD
https://scholar.archive.org/work/zopwejc7zff47do6mksp46jb5i
I describe the inception and development of nonperturbative OPE-based methods in hadronic physics, such as the SVZ sum rules, inverse heavy quark mass expansion (IHQME) and so on and related topics. Invited contribution to the EPJC Volume celebrating 50 years of Quantum Chromodynamics, to be published in December 2022.M. Shifmanwork_zopwejc7zff47do6mksp46jb5iMon, 19 Sep 2022 00:00:00 GMTS=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas
https://scholar.archive.org/work/f5zondr5ibaqnhbtrhi5qfqrea
We prove the S=T conjecture proposed by Xiao-Zhu in , making use of Scholze's theory of diamonds and v-stacks and Fargues-Scholze's geometric Satake equivalence. We deduce the Eichler-Shimura relation for Shimura varieties of Hodge type.Zhiyou Wuwork_f5zondr5ibaqnhbtrhi5qfqreaMon, 19 Sep 2022 00:00:00 GMTMackey profunctors
https://scholar.archive.org/work/3fefkligknbbzdhskm5omm23ve
We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.D. Kaledinwork_3fefkligknbbzdhskm5omm23veSun, 18 Sep 2022 00:00:00 GMTAn exact category approach to Hecke endomorphism algebras
https://scholar.archive.org/work/jdiw7jqjrze7bnfdxtmxfu7swq
Let G be a finite group of Lie type. In studying the cross-characteristic representation theory of G, the (specialized) Hecke algebra H=_G(_B^G1_B) has played a important role. In particular, when G=GL_n(𝔽_q) is a finite general linear group, this approach led to the Dipper-James theory of q-Schur algebras A. These algebras can be constructed over :=ℤ[t,t^-1] as the q-analog (with q=t^2) of an endomorphism algebra larger than H, involving parabolic subgroups. The algebra A is quasi-hereditary over . An analogous algebra, still denoted A, can always be constructed in other types. However, these algebras have so far been less useful than in the GL_n case, in part because they are not generally quasi-hereditary. Several years ago, reformulating a 1998 conjecture, the authors proposed (for all types) the existence of a -algebra A^+ having a stratified derived module category, with strata constructed via Kazhdan-Lusztig cell theory. The algebra A is recovered as A=eA^+e for an idempotent e∈ A^+. A main goal of this monograph is to prove this conjecture completely. The proof involves several new homological techniques using exact categories. Following the proof, we show that A^+ does become quasi-hereditary after the inversion of the bad primes. Some first applications of the result – e.g., to decomposition matrices – are presented, together with several open problems.Jie Du, Brian Parshall, Leonard Scottwork_jdiw7jqjrze7bnfdxtmxfu7swqFri, 16 Sep 2022 00:00:00 GMTThe 6-Functor Formalism for ℤ_ℓ- and ℚ_ℓ-Sheaves on Diamonds
https://scholar.archive.org/work/6yj2mjhs2bdtnmap3z6yjivgou
For every nuclear ℤ_ℓ-algebra Λ and every small v-stack X we construct an ∞-category 𝒟_nuc(X,Λ) of nuclear Λ-modules on X. We then construct a full 6-functor formalism for these sheaves, generalizing the étale 6-functor formalism for Λ = 𝔽_ℓ. Prominent choices for Λ are ℤ_ℓ, ℚ_ℓ and ℚ̅_̅ℓ̅ and especially in the latter two cases, no satisfying 6-functor formalism has been found before. Applied to classifying stacks we obtain a theory of nuclear representations, i.e. continuous representations on filtered colimits of Banach spaces.Lucas Mannwork_6yj2mjhs2bdtnmap3z6yjivgouFri, 16 Sep 2022 00:00:00 GMTTime symmetry in quantum theories and beyond
https://scholar.archive.org/work/bdrplrgyl5d7fdijbpwylqxqdu
There is a stark tension among different formulations of quantum theory in that some are fundamentally time-symmetric and others are radically time-asymmetric. This tension is crisply captured when thinking of physical theories as theories of processes. We review process theories and their diagrammatic representation, and show how quantum theory can be described in this language. The tension between time-symmetry and time-asymmetry is then captured by the tension between two of the key structures that are used in this framework. On the one hand, the symmetry is captured by a dagger structure, which is represented by a reflection of diagrams. On the other hand, the asymmetry is captured by a condition involving discarding which, ultimately, is responsible for the theory being compatible with relativistic causality. Next we consider three different ways in which we this tension can be resolved. The first of these is closely related to recent work of Lucien Hardy, where the tension is resolved by adding in a time reversed version of discarding together with a suitable consistency condition. The second is, to our knowledge, a new approach. Here the tension is resolved by adding in new systems which propagate backwards in time, and imposing a consistency condition to avoid running into well known time-travel paradoxes. The final approach that we explore is closely related to work of Oreshkov and Cerf, where the tension is resolved by removing the constraint associated with discarding. We show two equivalent ways in which this can be done whilst ensuring that the resulting theory still makes sensible operational predictions.John H. Selby, Maria E. Stasinou, Stefano Gogioso, Bob Coeckework_bdrplrgyl5d7fdijbpwylqxqduFri, 16 Sep 2022 00:00:00 GMTTopological symmetry in quantum field theory
https://scholar.archive.org/work/zykzvhif3fcufjmyv32ics7ake
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called "gauging" and "condensation defects"), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.Daniel S. Freed, Gregory W. Moore, Constantin Telemanwork_zykzvhif3fcufjmyv32ics7akeThu, 15 Sep 2022 00:00:00 GMTBounded solutions of KdV: uniqueness and the loss of almost periodicity
https://scholar.archive.org/work/fqrrt44en5d23a33ixfomu5tqu
We address two pressing questions in the theory of the Korteweg--de Vries (KdV) equation. First, we show the uniqueness of solutions to KdV that are merely bounded, without any further decay, regularity, periodicity, or almost periodicity assumptions. The second question, emphasized by Deift, regards whether almost periodic initial data leads to almost periodic solutions to KdV. Building on the new observation that this is false for the Airy equation, we construct an example of almost periodic initial data whose KdV evolution remains bounded, but fails to be almost periodic at a later time. Our uniqueness result ensures that the solution constructed is the unique development of this initial data.Andreia Chapouto, Rowan Killip, Monica Vişanwork_fqrrt44en5d23a33ixfomu5tquThu, 15 Sep 2022 00:00:00 GMTProbing light dark sector at future lepton colliders via (dark) Higgs invisible decays
https://scholar.archive.org/work/6dlvfk4kk5bodcrrrdyvsy5epm
A renormalizable UV model for Axion-Like Particles (ALPs) or hidden photons, that may explain the dark matter usually involves a dark Higgs field which is a singlet under the standard model (SM) gauge group. The dark sector can couple to the SM particles via the portal coupling between the SM-like Higgs and dark Higgs fields. Through this coupling, the dark sector particles can be produced in either the early universe or the collider experiments. Interestingly, not only the SM-like Higgs boson can decay into the light dark bosons, but also a light dark Higgs boson may be produced and decay into the dark bosons in a collider. In this paper, we perform the first collider search for invisible decays by taking both the Higgs bosons into account. We use a multivariate technique to best discriminate the signal from the background. We find that a large parameter region can be probed at the International Linear Collider (ILC) operating at the center-of-mass energy of 250 GeV. In particular, even when the SM-like Higgs invisible decay is a few orders of magnitude below the planned sensitivity reach of the ILC, the scenario can be probed by the invisible decay of the dark Higgs boson produced via a similar diagram. Measuring the dark Higgs boson decay into the dark sector will be a smoking gun signal of the light dark sector. A similar search of the dark sector would be expected in, e.g., Cool Copper Collider (C^3), Circular Electron Positron Collider (CEPC), Compact Linear Collider (CLIC) and Future Circular electron-positron Collider (FCC-ee).Gholamhossein Haghighat, Mojtaba Mohammadi Najafabadi, Kodai Sakurai, Wen Yinwork_6dlvfk4kk5bodcrrrdyvsy5epmThu, 15 Sep 2022 00:00:00 GMTEquivariant infinite loop space theory, the space level story
https://scholar.archive.org/work/g6bbyzjb2jcndooldwpuvwbgya
We rework and generalize equivariant infinite loop space theory, which shows how to construct G-spectra from G-spaces with suitable structure. There is a classical version which gives classical Ω-G-spectra for any topological group G, but our focus is on the construction of genuine Ω-G-spectra when G is finite. We also show what is and is not true when G is a compact Lie group. We give new information about the Segal and operadic equivariant infinite loop space machines, supplying many details that are missing from the literature, and we prove by direct comparison that the two machines give equivalent output when fed equivalent input. The proof of the corresponding nonequivariant uniqueness theorem, due to May and Thomason, works for classical G-spectra for general G but fails for genuine G-spectra. Even in the nonequivariant case, our comparison theorem is considerably more precise, giving an illuminating direct point-set level comparison. We have taken the opportunity to update this general area, equivariant and nonequivariant, giving many new proofs, filling in some gaps, and giving a number of corrections to results and proofs in the literature.J. Peter May, Mona Merling, Angélica M. Osornowork_g6bbyzjb2jcndooldwpuvwbgyaThu, 15 Sep 2022 00:00:00 GMT