Max Hübner

Department of Physics and Astronomy · David Rittenhouse Laboratory, 209 S 33rd St, Philadelphia, PA 19104 · hmax@sas.upenn.edu

My current home institution is the University of Pennsylvania where I hold the position of a postdoctoral researcher in the high energy theory group. My academic work focusses on the interplay of geometry with quantum field theories and quantum gravity. I am a member of the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics. I completed my DPhil at the University of Oxford 2021.

My CV serves as a summary of this website.

Links to my university webpage and inspire profile:

Preprints and Publications

Jonathan J. Heckman, MH, Chitraang Murdia 'On the Holographic Dual of a Topological Symmetry Operator', 2401.09538, January 2024, 22 pages
Abstract
We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p ≥ 0 in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (-m)-form symmetries for m ≥ 2.

Talks by authors: MH
Florent Baume, Jonathan J. Heckman, MH, Ethan Torres, Andrew P. Turner, Xingyang Yu 'SymTrees and Multi-Sector QFTs', 2310.12980, October 2023, 69 pages
Abstract
The global symmetries of a D-dimensional QFT can, in many cases, be captured in terms of a (D+1)-dimensional symmetry topological field theory (SymTFT). In this work we construct a (D+1)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly non-topological junctions. In string-realized multi-sector QFTs, these junctions are smoothed out in the extra-dimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large M averaging where the topological sectors of different large M replicas become dressed by additional extended operators associated with the SymTree.

Talks by authors: XY, ET, MH
Mirjam Cvetič, Jonathan J. Heckman, MH, Ethan Torres, 'Generalized Symmetries, Gravity and the Swampland', 2307.13027, July 2023, 62 pages
Abstract
Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity / the Swampland program, it is widely expected that all global symmetries are either gauged or broken, and this breaking is in turn related to the expected completeness of the spectrum of charged states in quantum gravity. We investigate the fate of such symmetries in the context of 7D and 5D vacua realized by compact Calabi-Yau spaces with localized singularities in M-theory. We explicitly show how gravitational backgrounds support additional dynamical degrees of freedom which trivialize (i.e.,"break") the higher symmetries of the local geometric models. Local compatability conditions across these different sectors lead to gluing conditions for gauging higher-form and (in the 5D case) higher-group symmetries. This also leads to a preferred global structure of the gauge group and higher-form gauge symmetries. In cases based on a genus-one fibered Calabi-Yau space, we also get an F-theory model in one higher dimension with corresponding constraints on the global form of the gauge group.

Talks by authors: JJH, MH, ET
Mirjam Cvetič, Jonathan J. Heckman, MH, Ethan Torres, 'Fluxbranes, Generalized Symmetries, and Verlinde's Metastable Monopole', 2305.09665 , Mai 2023, 23 pages
Abstract
The stringy realization of generalized symmetry operators involves wrapping "branes at infinity". We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde's monopole, a proposed particle which is BPS when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (resp. magnetic) confinement (resp. screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector.

Talks by authors:
Bobby Acharya, Michele Del Zotto, Jonathan J. Heckman, MH, Ethan Torres, 'Junctions, Edge Modes, and G2-Holonomy Orbifolds', 2304.03300, April 2023, 56 pages
Abstract
One of the general strategies for realizing a wide class of interacting QFTs is via junctions and intersections of higher-dimensional bulk theories. In the context of string/M-theory, this includes many D>4 superconformal field theories (SCFTs) coupled to an IR free bulk. Gauging the flavor symmetries of these theories and allowing position dependent gauge couplings provides a general strategy for realizing novel higher-dimensional junctions of theories coupled to localized edge modes. Here, we show that M-theory on singular, asymptotically conical G2-holonomy orbifolds provides a general template for realizing strongly coupled 5D bulk theories with 4D N=1 edge modes. This geometric approach also shows how bulk generalized symmetries are inherited in the boundary system.

Talks by authors: MDZ, MH
Jonathan J. Heckman, MH, Ethan Torres, Xingyang Yu, Hao Y. Zheng, 'Top Down Approach to Duality Defects', 2209.03343, December 2022, 41 pages
Abstract
Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D N=4 Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing X a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable SL(2, Z) transformation when they are crossed. Reduction on the boundary topology ∂X results in a 5D symmetry TFT. Different realizations of duality defects such as Kramers-Wannier-like and half-space gauging constructions simply amount to distinct choices of where to place the branch cuts in the 5D bulk.

Talks by authors: MH
Jonathan J. Heckman, MH, Ethan Torres, Hao Y. Zheng, 'The Branes Behind Generalized Symmetry Operators', 2209.03343, September 2022, 21 pages, Fortsch. Phys. 71 (2023) 1
Abstract
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. Line-like defects which are charged under a suitable 1-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

Talks by authors: MH, MH, ET
Mirjam Cvetič, Jonathan J. Heckman, MH, Ethan Torres, '0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds', 2203.10102, March 2022, 78 pages, Phys.Rev.D 106 (2022) 10
Abstract
Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determines global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities which extend to the boundary of the non-compact geometry. The resulting category of boundary conditions then captures these symmetries, and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including 5D superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via M-theory on non-compact G2 spaces.

Talks by authors: MC, JJH, MH, ET, MC
MH, David R. Morrison, Sakura Schäfer-Nameki, Yi-Nan Wang, 'Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations', 2203.10022, March 2022, 57 pages, SciPost Phys. 13 (2022) 030
Abstract
We realize higher-form symmetries in F-theory compactifications on non-compact elliptically fibered Calabi-Yau manifolds. Central to this endeavour is the topology of the boundary of the non-compact elliptic fibration, as well as the explicit construction of relative 2-cycles in terms of Lefschetz thimbles. We apply the analysis to a variety of elliptic fibrations, including geometries where the discriminant of the elliptic fibration intersects the boundary. We provide a concrete realization of the 1-form symmetry group by constructing the associated charged line operator from the elliptic fibration. As an application we compute the symmetry topological field theories in the case of elliptic three-folds, which correspond to mixed anomalies in 5d and 6d theories.

Talks by authors: MH
Lakshya Bhardwaj, Simone Giacomelli, MH, Sakura Schäfer-Nameki, 'Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S', 2201.00018, December 2021, 125 pages, SciPost Phys. 13 (2022) 101
Abstract
A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d N=(2,0) theories that are boundary conditions of 7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d N=(2,0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d N=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d N=2 Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.
Lakshya Bhardwaj, MH, Sakura Schäfer-Nameki, 'Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)', 2106.10265, June 2021, 86 pages, SciPost Phys. 12 (2022) 040
Abstract
We study confinement in 4d N=1 theories obtained by deforming 4d N=2 theories of Class S. We argue that confinement in a vacuum of the N=1 theory is encoded in the 1-cycles of the associated N=1 curve. This curve is the spectral cover associated to a generalized Hitchin system describing the profiles of two Higgs fields over the Riemann surface upon which the 6d (2,0) theory is compactified. Using our method, we reproduce the expected properties of confinement in various classic examples, such as 4d N=1 pure Super-Yang-Mills theory and the Cachazo-Seiberg-Witten setup. More generally, this work can be viewed as providing tools for probing confinement in non-Lagrangian N=1 theories, which we illustrate by constructing an infinite class of non-Lagrangian N=1 theories that contain confining vacua. The simplest model in this class is an N=1 deformation of the N=2 theory obtained by gauging SU(3) × SU(3) × SU(3) flavor symmetry of the E6 Minahan-Nemeschansky theory.

Talks by authors: LB, SSN
Lakshya Bhardwaj, MH, Sakura Schäfer-Nameki, '1-form Symmetries of 4d N=2 Class S Theories ', 2102.01693, Feb 2021, 62 pages, SciPost Phys. 11 (2021) 096
Abstract
We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

Talks by authors: LB, SSN
MH, 'Local G2-manifolds, Higgs bundles and a colored quantum mechanics', 2102.01693, Sep 2020, 61 pages, JHEP 05 (2021) 002
Abstract
M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

Talks by authors: MH
MH, '5d SCFTs from (En,Em) conformal matter', 2006.01694, June 2020, 31 pages, JHEP 12 (2020) 014
Abstract
We determine 5d N=1 SCFTs originating from 6d (En,Em) conformal matter theories with n ≠ m by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers.
Andreas P. Braun, Sebastjan Cizel, MH, Sakura Schäfer-Nameki, 'Higgs bundles for M-theory on G2-manifolds', 1812.06072, December 2018, 82 pages, JHEP 03 (2019) 199
Abstract
M-theory compactified on G2-holonomy manifolds results in 4d N = 1 supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle M3. We derive the BPS equations and find the massless spectrum for both abelian and non-abelian gauge groups in 4d. The mathematical tool that allows us to determine the spectrum is Morse theory, and more generally Morse-Bott theory. The latter generalization allows us to make contact with twisted connected sum (TCS) G2-manifolds, which form the largest class of examples of compact G2-manifolds. M-theory on TCS G2-manifolds is known to result in a non-chiral 4d spectrum. We determine the Higgs bundle for this class of G2-manifolds and provide a prescription for how to engineer singular transitions to models that have chiral matter in 4d.

Talks by authors: SSN

Talks



Education

University of Oxford

Doctor of Philosophy
Mathematics
Thesis: Higgs Bundles for 4d N=1 Gauge Theories
Advisor: Sakura Schäfer-Nameki
Oct. 2017 - Aug. 2021

University of Cambridge

Master of Advanced Studies
Applied Mathematics

Distinction

Thesis: Partition Functions of 2d Yang-Mills Theory
Advisor: David Skinner
Oct. 2016 - June 2017

University of Würzburg

Bachelor of Science
Mathematical Physics

Overall Mark: 1.00

Thesis: H → 2γ in the Two-Higgs-Doublet Model
Advisor: Ansgar Denner
Sept. 2013 - Sept. 2016

Awards

Marie Sklodowska-Curie Individual Fellowship (offered, 206,887.68 EUR)

Marie Skłodowska-Curie Actions (MSCA), a program funded under the European Union's Horizon 2020 initiative, is one of the largest European supporters of excellence in research and innovation. Awards fully cover postdoctoral expenses and salary for a self-determined research agenda lasting a period of 2 years. Acceptance rates usually vary between 10-15%.

June 2023

Oxford Mathematics Institute Scholarship

The Institute of Mathematics at the University of Oxford awards a small number of D.Phil. scholarships. Candidates are put forward by the individual research groups of the department and selected on merit.

Oct. 2020 - Aug. 2021

Promotionsstipendium der Studienstiftung des Deutschen Volkes

In addition to its undergraduate scholarship the Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) runs a separate and more competitive competition for doctoral scholarships. These are awarded for a maximum of 3 years and grant a living cost stipend.

Oct. 2017 - Sept. 2020

DAAD Scholarship for Studies Abroad

Among other endeavours the DAAD (German Academic Exchange Service) supports German undergraduates and graduate students in seeking international academic experience. Founded in 1925 it is the largest German support organisation in the field of international academic co-operation. On the basis of academic merit it awards a stipend at 800€/month, supports travel costs and covers tuition fees up to 6.100€.

Oct. 2016 - Sept. 2017

Stipendium der Studienstiftung for Studies Abroad

The Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) invites for applications to generously support 1-2 year undergraduate and master studies abroad. It awards a stipend of 350€/month, supports travel costs and covers up to 10.000€ of annual tuition fees.

Oct. 2016 - Sept. 2017

Max-Weber Scholarship

Max Weber was a German sociologist, jurist, and political economist and an influential theorists on the development of modern Western society. The Max-Weber Scholarship support German students studying at Bavarian universities. The programm emphasizes the personal development of students. In conjunction with academic support it awards a stipend of 215€/month.

April 2015 - Sept. 2017

Scholarship of the Studienstiftung des Deutschen Volkes

The Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) is Germany's largest and oldest scholarship foundation. It was founded in 1925 with the goal to support promising individuals. The Studienstiftung is non-political, non-denominational and ideologically independent. The scholarship is awarded to less than 0.5% of all students annually and includes a stipend of 300€/month and academic support.

April 2015 - Sept. 2017

Deutschlandstipendium

Introduced in 2011 the Deutschlandstipendium is a scholarship awarded to university students at German universities for academic excellence. An average of 1.5% of all students are awarded this scholarship annually. It awards a stipend of 300€/month and offers academic support.

Oct. 2014 - Oct. 2015

Teaching

I taught at various Oxford colleges and in the Mathematics Department at Oxford University. Currently I do not teach.

Skills and Interests

Wonderfully, I was able to spend 6 years of my childhood in Canberra and Melbourne, Australia. I am fluent in both German and English. I enjoy ballroom dancing, athletics and playing the piano.