Michaelmas 2019

http://www2.physics.ox.ac.uk/research/particle-theory

Applicants resident in the UK will usually be called for interview in March; overseas applicants may be interviewed by phone/skype. Preliminary offers (subject to satisfactory examination results) are made at this time, both for places and for STFC studentships.

Oxford Particle Theory Group Founded in 1963 by Richard (Dick) Dalitz Former members: Jack Paton, Ian Aitchison, John Taylor, Chris Llewellyn- John Wheater 1986- Smith, Frank Close, *, Mike Andrei Starinets 2008- Conformal field theory Teper*, Giulia Zanderighi, Uli Haisch Gauge-string duality, & quantum gravity holography, AdS-CFT + presently 6 postdocs & ~15 DPhil students

+ Visitors: Christopher Herzog (KCL) Stephen West (RHUL) Lorenzo Tancredi RSURF 2019- Andre Lukas 2004- + Many associates in Astro, PP & Maths Inst String theory and phenomenology Supported by: UKRI, EU, Royal Society …

Lucian Harland-Lang ERF 2017-

Subir Sarkar 1990/98- Joe Conlon 2008/14- John March-Russell 2002- Gavin Salam 2018- Fabrizio Caola 2019- Particle astrophysics beyond the Phenomenology of EW & strong interactions and cosmology Standard Model Oxford alumnus shares Nobel Prize in Physics 2016 Staff

JOSEPH CONLON

String theory and compactifications String phenomenology Also interested in astroparticle physics, cosmology and BSM Current interest: the swampland – how does ultraviolet consistency constrainJoe low-energy effective Conlon Lagrangians? Students: Filippo Revello (2nd year), Sirui Ning (1st year)

Andre Lukas Main interest: string theory, with emphasis on compactifications, model building and phenomenology. More specifically: • Calabi-Yau manifolds, vector bundles and heterotic model building • Flux compactifications and non-CY manifolds

• Machine learning andAll this string suggests a di↵erent theory approach to machine learning of line bundle cohomology which incor- porates information about the mathematical structure of the problem. This is what we turn to • M-theory compactificationsnow. and F-theory • String cosmology 4 Learning cohomology formulae As discussed earlier, there are strong indications that cohomology dimensions can be described in terms of a relatively simple mathematical structure. The Picard lattice is divided into regions - fre- quently, but not always cones - in each of which the cohomology dimensions are given by a polynomial Major theme: “Gettingwith the degree equal standard to the complex dimension model of the manifold. Thisfrom behaviour hasstring been empirically theory” observed for a number of examples [11,15], including surfaces and three-folds, and it has been proven for classes of surfaces [14] as well as for some three-folds, such as the bi-cubic [11]. Our hypothesis For example arXiv:1906.08730: here is simply that this structure is fairly general and in particular applies to all examples we will study. Where currently no mathematical proof is available, further evidence for the hypothesis will

in fact be provided by the approach to machine learning discussed in this section. region 1 Machine Learning Line Bundle Cohomology region 2 region 1 4.1 Network structure region 3 region 2 10 10 10 region 4 region 3 k2 k 10 The structure of the network we will be using0 is indicated in Fig. 4. 2 0 1 2 1 1 k 10 region 4 10 2 0 region 5 k2 Callum R. Brodie , Andrei Constantin , Rehan Deen , Andre Lukas 10 0 -10 region-10 5 10 -10 region 6 -10 0 region 6 k 0 -10 1 not0identified -10 k1 0 1 k1 not identified k Rudolf Peierls Centre for Theoretical Physics, , -10 -10 1 0 0 Parks Road, Oxford OX1 3PU, UK 0 h n1 n1 n2 -10 0 -10 k0 -10 k0 -10 Z R R R k0 n2 k0 k (W1, b1) (W , b ) 10 10 2 2 R 10 10 2Pembroke College, University of Oxford, OX1 1DW, UK R Mansfield College, University of Oxford, OX1 3TF, UK Figure 6: RegionsFigure in the 6: PicardRegions lattice in the for Picard the lattice zeroth for cohomology the zeroth cohomology of dP2, determined of dP , determined from the from trained the network trained network in in n2 2 Fig. 4 for (n1,n2Fig.)=(84 for, 8)(nand1,n2 a)=(8 trainingR , 8) and box a of training size kmax box of= size15.k Themax figure= 15. The on the figure left on shows the left the shows regions the regionsobtained obtained N after step (2) ofafter theZ algorithm. step (2) of theThe algorithm. figure on· The the figure right onshows the rightthe “cleaned-up” shows the “cleaned-up” regions obtained regions obtained after step after (4) step of (4) of x =(ki,kikj,...) the algorithm.(W3, b3) The legend labels the regions as in Eqs. (4.3), (4.4) Abstract g the algorithm. The legend labels the regions as in Eqs. (4.3), (4.4) We investigate di↵erent approaches to machine learning of line bundle cohomology on complex polynomial fit topolynomial each of thefit to six each regions of the (step six regions (3) of (step the algorithm)(3) of the algorithm) leads to leads to surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully Figure 4: Structure of the network to learn piecewise polynomial cohomology formulae. The dot in the element connected networks with logistic sigmoids is reviewed and its main features and shortcomings are 1+ 3 k + 1 k2 + 1 k 1 k2 + 1 k 1 k2 in region 1 , on the right indicates a dot product, taken between the two input vectors. 3 1 2 2 10 2 10 2 2 11 2 11 22 2 2 2 discussed. It has been observed recently that line bundle cohomology can be described by dividing 1+ 2 k0 + 2 k0 + 2 k1 2 2 k1 + 2 k2 2 k2 in region 1 , 81+2k0 +k + k1 + k0k1+ k2 + k0k2 + k1k2 in region 2 , the Picard lattice into certain regions in each of which the cohomology dimension is described 2 0 Let us discuss how this network relates to the underlying mathematical81+2 structurek0 + k>0 of+ k line31 + bundlek01k12 + k1 2 + k10k22 + k1k2 in region 2 , >1+ k0 + k + k2 k in region 3 , by a polynomial formula. Based on this structure, we set up a network capablecohomology. of identifying The training data used for this network is of the formh (2.160>( ), that(3k)) is = we>1 are2 adding2 1 2 the10 2 2 2 2 (4.3) >1+dP2 k0 + >k +3 k2 1 2k 1 1 2 in region 3 , the regions and their associated polynomials, thereby e↵ectively generating a conjecture for the 0 >O 2 >2 1+0 k20 + k20 +2 k1 k1 in region 4 , monomials kikj and, for three-folds, also the monomialsh ( dPkik2j(kkl ))to = the> input vector>ki, so2 that2 the 2 2 (4.3) > 3 <1 2 3 1 1 1 2 correct cohomology formula. For complex surfaces, we also set up a network which learns certain O >1+ k0 + k1+0 + kk+1 k2k1 in regionin 4 region, 5 . problem becomes e↵ectively piecewise linear. > 2 2 2 20 2 20 rigid divisors which appear in a recently discovered master formula for cohomology dimensions. < 3 >1 2 The upper part of the network in Fig. 4, denoted by g✓,where✓ =(W1+1, b1,Wk02+, b>2),k00 is a two-layer in region in 5 region. 6 . 2 >2 network with n1 and n2 neurons in each layer, whose input is simply> the vector k.> We can think of >0> in region 6 . the output, g✓(k) as a “binary code” which indicates theUsing region these within equations> which to the determine: vector k theresides. exact regions (step (4)) leads to the plot on the right-hand- In other words, this upper branch of the network detects the various> regions in the Picard lattice. Using these equationsside of Fig. to6 determine.:> In step (5), the we exact thenregions determine (step the inequalities(4)) leadsto which the describe plot on those the right-hand- regions. They are Current students: Stefan Blasneag,The width Callum (n1,n2) of this Brodie, network should be Pandora of the ordergiven of by the expectedDominiak number of regions. The underlying assumption is that the regionsside are of Fig.given6 as. In intersections step (5), we of half-spaces, then determine which theis the inequalities case which describe those regions. They are for most examples studied to date. given by Region 1: k1 0 k2 0 k0 + k1 + k2 0 The lower part of the network is a simple linear layer withRegionn neurons 2: and weights/biases (Wk0, b+)k1 + k2 < 0 k0 + k1 0 k0 + k2 0 2 3 3 which represent the coecients of the variousRegion polynomial 1: kRegion equations.1 0 3: Byk2k multiplying<00 k0 +k thesek1 +0 weightsk2 0 k + k 0 1 2 0 2 (4.4) into the monomial input vector x =(k ,kRegionk ,...) this 2: layerRegion outputs 4: a vectork which0 k0 +k consistsk<1 +0 k of2 < the0 k0 + k1 0 k0 + k2 k 0+ k 0 i i j 1 2 0 2 values of n2 polynomials in k. Dotting thisRegion vector into 3: thekRegion “binary< 0 5: vector”k k1 from<00 thek upper2 < 0 network k + k 0 k0 0 1 2 0 2 (4.4) selects the specific linear combination of polynomialsRegion 4: associatedkRegion to0 6: the regionotherwisek < 0 in which k resides. k + k 0 1 2 0 2 Region 5: k < 0 k < 0 k 0 In summary,1 the network2 has learned the formula for the dimensions of the zeroth0 line bundle coho- Region12 6: otherwise mology on dP2. By applying the master formula (2.4)todP2, it can be shown that the above result arXiv:1906.08730v1 [hep-th] 20 Jun 2019 is indeed correct on the entire Picard lattice. The explicit proof can be found in Ref. [15]. In summary, the network has learned the formula for the dimensions of the zeroth line bundle coho- mology on dP2We. By would applying like to the analyse master two formula further ( surface2.4)todP examples2, it can for bewhich shown cohomology that the formulae above result are not yet is indeed correctknown. on the They entire are Picard CI manifolds lattice. defined Theby explicit the configuration proof can be matrices found in Ref. [15]. 1 2 1 3 We would like to analyse two further surfaceX examplesP for,Y which cohomologyP . formulae are not yet (4.5) 2 P2 3 2 P2 4 known. They are CI manifolds defined by the configuration matrices The first of these, X, is a K3 surface, while Y is a surface of general type with an ample canonical [email protected] P1 2 P1 3 bundle. For bothX cases, the rank of,Y the Picard lattice is two. and line bundles are denoted(4.5) by (k), andrei.constantin@mansfield.ox.ac.uk 2 P2 3 2 P2 4 O [email protected] where k =(k1,k2). The results for the K3 example are shown in Fig. 7. As is evident, the network [email protected] The first of these,identifiesX, is two a K3 large surface, regions. while We canY is also a surface see a new of phenomenongeneral type emerging with an which ample does canonical not arise for manifolds with an ample anti-canonical bundle. There are lower-dimensional regions, in the present bundle. For both cases, the rank of the Picard lattice is two and line bundles are denoted by (k), O where k =(k ,k ). The results for the K3 example are shown in Fig. 7. As is evident, the network 1 2 15 identifies two large regions. We can also see a new phenomenon emerging which does not arise for manifolds with an ample anti-canonical bundle. There are lower-dimensional regions, in the present

15 John March-Russell

• Mystery of the Higgs & the Weak Scale: Approaches to the “Hierarchy Problem” — (non-minimal) supersymmetry? — unusual strong-coupling dynamics? —new symmetries? — extra dimensions? — physical naturalness? • Dark matter: What is it? How does it interact with SM sector? Unusual/ Johnnew observationalMarch signals? New Russell production mechanisms? • Strong CP problem: Is the Peccei-Quinn axion the solution or something new? Are there other super-light weakly coupled bosons like axion? How to discover them? • Gauge unification? String Theory pheno? Family replication? CP-violation? Hidden Sectors? Gravity Waves? Inflation? Baryogenesis? Why 4D? Cosmo constant?…

Students: Giacommo Marocco (with J Wheater), Konstantin Beyer (with G Gregori, ALP)

Neutrinos: I am a member (since 2004) of the IceCube experiment which discovered cosmic high energy neutrinos … my interest is in High-energy neutrino cross section studying deep inelastic scattering at energies beyond the reach of Frequentist result Bayesian result the LHC (e.g. our prediction using HERAPDF has been confirmed 7 upto En ~10 GeV ➛ ruling out new physics up to ~10 TeV scale). Also studying effects of QG-induced decoherence on n oscillations. arXiv:1908.07027 Dark matter: Currently interested in axions (contribution to relic abundance from axion domain walls and strings) … also new laboratory detection techniques (in QTFP programme). Results consistent with SM prediction 10 5 ΛCDM reconstruction Early universe: Reconstruction of the spectrum of primordial Power law 4 1σ credible interval )

k 1σ confidence interval scalar fluctuations from CMB and other datasets shows spectral ( :049,2019 P 7 9 3 features which may be evidence for multiple episodes of inflation 10 … we provide a dictionary to map on to (time-dependence of) the 2 SciPost

5 4 3 2 1 0 relevant parameters in the Effective Field Theory of inflation. 10− 10− 10− 10− 10− 10 1 k (Mpc− ) Late universe: The acceleration of the Hubble expansion rate deduced from Type Ia Supernovae is very anisotropic - being mainly along the direction of our local ‘bulk flow’ … the evidence for an isotropic component (⇒ ‘dark energy’) is only 1.4s! (All will be revealed at next Saturday’s Morning of Theoretical Physics) A&A, in [1808.04597]press AdS-CFT correspondence Gauge -gravity duality Gauge-string duality Holography

conjectured exact equivalence

Open strings picture: dynamics of strings Closed strings picture: dynamics of strings & branes at low energy is desribed by & branes at low energy is described by a quantum field theory without gravity string theory in curved space in higher dim.

STRONG COUPLING WEAK COUPLING Allows study of correlation functions, Wilson loops, thermodynamics, transport, non-equilibrium behavior, turbulence, quantum quenches etc in STRONGLY interacting systems (of some class) by using their DUAL weak gravity description Oxford Holography Group: B.Meiring, C.Herzog (long-term visitor), A.Starinets

John Wheater

Discretised models of Quantum Gravity and Quantum Geometry

Metrics on Manifolds Random Graph Ensembles s′′ s′′ s′ s′′′ s′′ ′ s′′ ′ ′ s s s′ Dgμν ∼ ∑ ∫ graphs

a) b) Global geometrical properties; Phases; Allowed boundary states

Students: Aravinth Kulantaivelu, “Dennis” Xavier Parveen, Collaborators: Bergfinnur Durhuus, , and Thordur Jonsson, Reykjavik Use of Quantum Detectors as probes of fundamental interactions Use the extraordinary precision capability of quantum device technology to measure tiny deviations from expected behaviour and thus probe BSM physics in regimes inaccessible to usual methods such as LHC. Student: Giacomo Marocco (with Subir Sarkar) Emeriti & Visitors Graham Ross - USS research fellow

Current interests:

• Scale invariance and the Standard Model plus Gravity

M H , M , Λ Pedro Ferreira, Chris Hill, Johannes Noller Planck, Inflation W C.C. Asymptotic safety … perhaps gravity cures all ills:

Landau pole, ghosts, cosmological constant, SM parameters

• Fermion masses and mixings

Complete description of quark, charged lepton and neutrinos based on

u,d ,l,ν SO(10) (27) U(1) : M Ivo Medeira Varzielas, Jim Talbert ⊗ Δ ⊗ Dirac ~universal

(we plan to extend this to a particular orbifold model with 3 families and Δ ( 54 ) family symmetry) Michael Teper

Research: non-perturbative properties of field theories important tool - lattice field theory

Publications (last year) : • Glueball Spins in D=3 Yang-Mills (arXiv:1909.07430, JHEP: P. Conkey, S. Dubovsky, MT) • On the spectrum and string tension of U(1) lattice gauge theory in 2+1 dimensions (arXiv:1811.06280, JHEP: A. Athenodorou, MT) • Pfaffian particles and strings in SO(2N) gauge theories (arXiv:1810.04546, JHEP: MT)

Main current project : Precise calculation of glueball spectrum (all cubic irreps)andspectrumof winding confining flux tubes in D=3+1 SU(N) gauge theories (with θ) (with A. Athenodorou)

1 Postdocs Rehan Deen Bio: Henry Skynner Research Fellow at Balliol Ph.D. at University of Pennsylvania Interests: I String model building: Constructing standard models from smooth heterotic compactifications – Moduli stabilization I Cosmology from string theory: Dynamics of moduli in quintessence and inflation – Bouncing cosmologies – Hidden sector dynamics + dark matter in het. M-theory Past + current projects: I SUSY phenomenology: R-parity violating B L MSSM - arXiv:1604.08588 I Cosmology:Sneutrino-higgsinflatonmodel,reheating–arXiv:1606.00431, arXiv:1804.07848 I Higher derivative SUSY/SUGRA:Analoguesofgalileons,dynamical auxiliary fields – arXiv:1705.06729, arXiv:1707.05305 I Machine Learning applications in String Theory: Cohomologies of surfaces –arXiv:1906.08730, Micro-landscape of heterotic line bundle models on CICYs Federico Buccioni Postdoctoral Research Assistant, Theoretical Physics Group: Prof. Fabrizio Caola Area of research: Precision Collider Phenomenology

PhD in Sep 2019 at the University of Zurich "A novel One-Loop Algorithm for Precision Phenomenology at High-Energy Colliders"

Mixed corrections to vector boson production

OpenLoops 1 One-loop automation the loop on-the-fly OpenLoops 2 is cut open algorithm

Multiparticle processes at the LHC Heavy quark phenomenology Frédéric Dreyer LHC Phenomenology

● Jet substructure and boosted object tagging at the LHC.

● Applications of machine learning in jet physics. ● Accuracy Fredricof parton showers and Dreyer connection with resummation.

● Higgs physics and fixed order QCD corrections. Michael Duerr: STFC PDRA

Beyond the Standard Model / Dark Matter phenomenology

thermal freeze-out (early Univ.) indirect detection (now)

DM SM > Gauge extensions of the SM direct detection

Model building, e.g., GSM U(1)B U(1)L DM SM ⌦ ⌦ production at colliders Low-scale breaking of U(1)B: testable > Consistent simple DM models Add the minimal amount of structure to the SM that is necessary to explain DM How simple can these setups be?

> Extended dark sectors Interesting experimental signatures How to test them at colliders? preliminary

Interested in many other things: axions, neutrinos, . . . Alexander Karlberg

QCD Phenomenology • Fixed order N(N)NLO calculations for LHC and future colliders • Matching of N(N)LO and Parton Showers • Understanding of infrared QCD through resummation (MiNLO) • Higgs/EWSB (VBF/VBS and boosted Higgs) • Back in Oxford to work on Parton Shower accuracy within the ERC funded PanScales project

Associates String Theory Group (Maths Branch)

✴ James Sparks ; AdS/CFT ✴ Chris Beem ; N=4 SYM, conformal field theories ✴ Fernando Alday ; integrability, strong coupling limit of N=4 SYMMathematics ✴ Lionel Mason and Andrew Hodges ; twistor string theory, amplitudesPhilip of N=4 Candelas SYM ✴ Sakura Schafer-Nameki ; F-theory, heterotic string theory ✴ Xenia de la Ossa and PC ; CY manifolds and heterotic string theory, non-Kähler manifolds