Dr Congkao WenRoyal Society University Research Fellow | Senior LecturerEmail: c.wen@qmul.ac.ukTelephone: 207 882 5923Room Number: G. O. Jones Building, Room 613ProfileTeachingResearchPublicationsSupervisionProfileI joined the Centre for Theoretical Physics (CTP) in 2018. Previously, I held research positions at Caltech, at University of Rome, Tor Vergata, and at CTP in QMUL. I recieved my PhD at Brown University, and I did my undergraduate and graduate studies at Zhejiang University.TeachingI currently teach a module `An introduction to strings and branes`. The course is a basic introduction to String theory and Branes. I also supervise undergraduate and master projects.ResearchResearch Interests:My recent research interest focuses on perturbative and non-perturbative aspects of quantum field theory, quantum gravity and string theory. One of my main areas of activity has been developing and exploiting modern powerful techniques of scattering amplitudes, which includes two main research directions: 1. new formulations of scattering amplitudes in terms of twistor theory and Grassmannian geometry; 2. applying modern techniques of scattering amplitudes to other research areas. Over the past few years, new twistor-like formulas have been discovered for scattering amplitudes in a wide range of interesting theories, including the world-volume theory of single probe brane in M-theory and string theory. These new mathematical formulas not only provide concrete formulas for the amplitudes in these theories, but also reveal new structures. This research direction is to discover such new formulations for more theories and explore the implications. My other major line of work is to study the applications of scattering amplitude techniques in other research areas. In particular, I am interested in understanding the symmetry constraints on effective actions in the language of scattering amplitudes. Scattering amplitudes provide extremely efficient ways of imposing the constraints, in the form of, for instance, soft theorems, unitarity and superamplitude consistency. Recently, I have also been interested in exploring deep connections between flat-space amplitudes and holographic correlation functions in AdS space. Holographic correlators resemble many properties of flat-space scattering amplitudes, especially when formulated in Mellin space. This allows us to apply "amplitude-inspired methods" to study these correlators at the level of supergravity limit and beyond. Examples of research funding:Grants held at QMUL as PI: Royal Society University Research Fellowship, 2018 - 2022 (£430,693) Royal Society Grant supporting a PhD Studentship, 2018 - 2022 (£92,148) Royal Society Grant supporting a PhD Studentship, 2022-2024 (£52,218) Royal Society University Research Fellowship Renewals, 2023- 2025 (£356,623) Royal Society Grant supporting a postdoc, 2023-2025 (£240,000)PublicationsMy list of publications: Complete list of publications on INSPIRE-HEP. Google Scholar data Chen G, Rodina L, Wen C (2024). Kinematic Hopf algebra and Bern-Carrasco-Johansson numerators at finite α′. nameOfConference DOI: 10.1103/physrevd.110.l041902 QMRO: qmroHref Brown A, Galvagno F, Wen C (publicationYear). Exact results for giant graviton four-point correlators. nameOfConference DOI: 10.1007/jhep07(2024)049 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/99026 Alday LF, Chester SM, Dorigoni D et al. (publicationYear). Relations between integrated correlators in N = 4 supersymmetric Yang-Mills theory. nameOfConference DOI: 10.1007/jhep05(2024)044 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/99025 Brown A, Heslop P, Wen C et al. (2024). Integrated Correlators in N=4 Supersymmetric Yang-Mills Theory beyond Localization. nameOfConference DOI: 10.1103/physrevlett.132.101602 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/95644 Chen G, Rodina L, Wen C (publicationYear). Kinematic Hopf algebra for amplitudes from higher-derivative operators. nameOfConference DOI: 10.1007/jhep02(2024)096 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/95645 Brown A, Wen C, Xie H (publicationYear). Generating functions and large-charge expansion of integrated correlators in 𝒩 = 4 supersymmetric Yang-Mills theory. nameOfConference DOI: 10.1007/jhep07(2023)129 QMRO: qmroHref Brown A, Wen C, Xie H (publicationYear). Laplace-difference equation for integrated correlators of operators with general charges in N = 4 SYM. nameOfConference DOI: 10.1007/jhep06(2023)066 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/89118 Dorigoni D, Green MB, Wen C et al. (publicationYear). Modular-invariant large-N completion of an integrated correlator in N = 4 supersymmetric Yang-Mills theory. nameOfConference DOI: 10.1007/jhep04(2023)114 QMRO: qmroHref Chen G, Lin G, Wen C (2023). Kinematic Hopf algebra for amplitudes and form factors. nameOfConference DOI: 10.1103/physrevd.107.l081701 QMRO: qmroHref Brandhuber A, Brown GR, Chen G et al. (2022). Amplitudes, Hopf algebras and the colour-kinematics duality. nameOfConference DOI: 10.1007/jhep12(2022)101 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/83931 Travaglini G, Brandhuber A, Dorey P et al. (2022). The SAGEX review on scattering amplitudes. nameOfConference DOI: 10.1088/1751-8121/ac8380 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/83486 Dorigoni D, Green MB, Wen C (2022). Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals. nameOfConference DOI: 10.1088/1751-8121/ac9263 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/83493 Dorigoni D, Green M, Wen C (2022). Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups. nameOfConference DOI: 10.21468/scipostphys.13.4.092 QMRO: qmroHref Dorigoni D, Green MB, Wen C (2022). Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups. nameOfConference DOI: 10.21468/scipost.report.5244 QMRO: qmroHref Wen C, Zhang S-Q (2022). Integrated correlators in N = 4 super Yang-Mills and periods. nameOfConference DOI: 10.1007/jhep05(2022)126 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/79129 Dorigoni D, Green MB, Wen C (2022). Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups. nameOfConference DOI: 10.21468/scipost.report.4990 QMRO: qmroHref Brandhuber A, Chen G, Johansson H et al. (2022). Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory. nameOfConference DOI: 10.1103/physrevlett.128.121601 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/78378 Huang YT, Kojima R, Wen C et al. (2022). The orthogonal momentum amplituhedron and ABJM amplitudes. nameOfConference DOI: 10.1007/JHEP01(2022)141 QMRO: qmroHref Dorigoni D, Green MB, Wen C (2021). Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) N = 4 SYM. nameOfConference DOI: 10.1007/jhep11(2021)132 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/76224 Brandhuber A, Chen G, Travaglini G et al. (2021). Classical gravitational scattering from a gauge-invariant double copy. nameOfConference DOI: 10.1007/JHEP10(2021)118 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/75160 Wen C, Zhang SQ (2021). Notes on gravity multiplet correlators in AdS 3 × S 3. nameOfConference DOI: 10.1007/JHEP07(2021)125 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/73371 Brandhuber A, Chen G, Travaglini G et al. (2021). A new gauge-invariant double copy for heavy-mass effective theory. nameOfConference DOI: 10.1007/jhep07(2021)047 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/73369 Dorigoni D, Green MB, Wen C (2021). Exact properties of an integrated correlator in N = 4 SU(N) SYM. nameOfConference DOI: 10.1007/JHEP05(2021)089 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/72566 Dorigoni D, Green MB, Wen C (2021). Novel Representation of an Integrated Correlator in N=4 Supersymmetric Yang-Mills Theory. nameOfConference DOI: 10.1103/physrevlett.126.161601 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/72565 Chester SM, Green MB, Pufu SS et al. (2021). New modular invariants in N = 4 Super-Yang-Mills theory. nameOfConference DOI: 10.1007/JHEP04(2021)212 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/72258 Green MB, Wen C (2021). Maximal U(1)Y-violating n-point correlators in N = 4 super-Yang-Mills theory. nameOfConference DOI: 10.1007/jhep02(2021)042 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/70499 Chester SM, Green MB, Pufu SS et al. (2020). Modular invariance in superstring theory from N = 4 super-Yang-Mills. nameOfConference DOI: 10.1007/JHEP11(2020)016 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/72262 Giusto S, Russo R, Tyukov A et al. (2020). The CFT6 origin of all tree-level 4-point correlators in AdS3 x S3. nameOfConference DOI: 10.1140/epjc/s10052-020-8300-4 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/66753 Wen C, Zhang S-Q (2020). D3-brane loop amplitudes from M5-brane tree amplitudes. nameOfConference DOI: 10.1007/jhep07(2020)098 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/75165 Green MB, Wen C (2019). Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values. nameOfConference DOI: 10.1007/jhep11(2019)079 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/61859 Giusto S, Russo R, Tyukov A et al. (2019). Holographic correlators in AdS3 without Witten diagrams. nameOfConference DOI: 10.1007/jhep09(2019)030 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/59720 Schwarz JH, Wen C (2019). Unified formalism for 6D superamplitudes based on a symplectic Grassmannian. nameOfConference DOI: 10.1007/jhep08(2019)125 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/59518 Chen W-M, Huang Y-T, Noumi T et al. (2019). Unitarity bounds on charged/neutral state mass ratios. nameOfConference DOI: 10.1103/physrevd.100.025016 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/59065 Green MB, Wen C (2019). Modular forms and SL(2, ℤ)-covariance of type IIB superstring theory. nameOfConference DOI: 10.1007/JHEP06(2019)087 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/58557 WEN C, Heydeman M, Schwarz JH et al. (2019). All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space. nameOfConference DOI: 10.1103/PhysRevLett.122.111604 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/56528 WEN C, Giusto S, RUSSO R (2019). Holographic correlators in AdS3. nameOfConference DOI: 10.1007/JHEP03(2019)096 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/56529 WEN C, Huang Y-T, Kuo C-K (2018). Dualities for Ising networks. nameOfConference DOI: 10.1103/PhysRevLett.121.251604 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/54102 WEN C, Cachazo F, Guevara A et al. (2018). The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps. nameOfConference DOI: 10.1007/JHEP09(2018)125 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/48444 Cheung C, Kampf K, Novotny J et al. (2018). Vector Effective Field Theories from Soft Limits. nameOfConference DOI: 10.1103/PhysRevLett.120.261602 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/48445 Cheung C, Remmen GN, Shen C-H et al. (2018). Pions as gluons in higher dimensions. nameOfConference DOI: 10.1007/JHEP04(2018)129 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/47927 Cheung C, Shen C-H, Wen C (2019). Unifying relations for scattering amplitudes. nameOfConference DOI: 10.1007/jhep02(2018)095 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/59519 Billò M, Fucito F, Lerda A et al. (2018). Two-point correlators in N = 2 gauge theories. nameOfConference DOI: 10.1016/j.nuclphysb.2017.11.003 QMRO: qmroHref Guerrieri AL, Huang Y-T, Li Z et al. (2017). On the exactness of soft theorems. nameOfConference DOI: 10.1007/jhep12(2017)052 QMRO: qmroHref WEN C, Schwarz J, Heydeman M (2017). M5-brane and D-brane scattering amplitudes. nameOfConference DOI: 10.1007/JHEP12(2017)003 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/36714 Bianchi M, Jantzen RT, Ruffini R et al. (2017). Instanton corrections to the effective action of 𝒩 = 4 SYM. The Fourteenth Marcel Grossmann Meeting DOI: 10.1142/9789813226609_0558 QMRO: qmroHref Meidinger D, Nandan D, Penante B et al. (2017). A note on NMHV form factors from the Graßmannian and the twistor string. nameOfConference DOI: 10.1007/jhep09(2017)024 QMRO: qmroHref Gliozzi F, Guerrieri AL, Petkou AC et al. (2017). The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points. nameOfConference DOI: 10.1007/jhep04(2017)056 QMRO: qmroHref Gliozzi F, Guerrieri AL, Petkou AC et al. (2017). Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion. nameOfConference DOI: 10.1103/PhysRevLett.118.061601 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/39591 Nandan D, Plefka J, Schlotterer O et al. (2016). Einstein-Yang-Mills from pure Yang-Mills amplitudes. nameOfConference DOI: 10.1007/JHEP10(2016)070 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/39587 Bianchi M, Guerrieri AL, Huang Y-T et al. (2016). Exploring soft constraints on effective actions. nameOfConference DOI: 10.1007/jhep10(2016)036 QMRO: qmroHref Bourjaily JL, Franco S, Galloni D et al. (2016). Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams. nameOfConference DOI: 10.1007/jhep10(2016)003 QMRO: qmroHref Huang Y-T, Schlotterer O, Wen C (2016). Universality in string interactions. nameOfConference DOI: 10.1007/jhep09(2016)155 QMRO: qmroHref Guerrieri AL, Petkou AC, Wen C (2016). The free σCFTs. nameOfConference DOI: 10.1007/jhep09(2016)019 QMRO: qmroHref Luo H, Wen C (2016). Recursion relations from soft theorems. nameOfConference DOI: 10.1007/jhep03(2016)088 QMRO: qmroHref Huang Y-T, Wen C (2015). Soft theorems from anomalous symmetries. nameOfConference DOI: 10.1007/jhep12(2015)143 QMRO: qmroHref Bianchi M, Morales JF, Wen C (2015). Instanton corrections to the effective action of N=4 SYM. nameOfConference DOI: 10.1007/jhep11(2015)006 QMRO: qmroHref Bianchi M, He S, Huang Y-T et al. (2015). More on soft theorems: Trees, loops, and strings. nameOfConference DOI: 10.1103/physrevd.92.065022 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/36713 Chen W-M, Huang Y-T, Wen C (2015). Exact coefficients for higher dimensional operators with sixteen supersymmetries. nameOfConference DOI: 10.1007/jhep09(2015)098 QMRO: qmroHref Volovich A, Wen C, Zlotnikov M (2015). Double soft theorems in gauge and string theories. nameOfConference DOI: 10.1007/JHEP07(2015)095 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/39590 Chen W-M, Huang Y-T, Wen C (2015). New Fermionic Soft Theorems for Supergravity Amplitudes. nameOfConference DOI: 10.1103/PhysRevLett.115.021603 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/39665 Franco S, Galloni D, Penante B et al. (2015). Non-planar on-shell diagrams. nameOfConference DOI: 10.1007/jhep06(2015)199 QMRO: qmroHref Chen W-M, Huang Y-T, Wen C (2015). From U(1) to E8: soft theorems in supergravity amplitudes. nameOfConference DOI: 10.1007/jhep03(2015)150 QMRO: qmroHref He S, Huang YT, Wen C (2014). Loop corrections to soft theorems in gauge theories and gravity. nameOfConference DOI: 10.1007/JHEP12(2014)115 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/36715 Garner D, Ramgoolam S, Wen C (publicationYear). Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5. nameOfConference DOI: 10.1007/JHEP11(2014)076 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/12419 Huang Y-T, Wen C, Xie D (2014). The positive orthogonal Grassmannian and loop amplitudes of ABJM. nameOfConference DOI: 10.1088/1751-8113/47/47/474008 QMRO: qmroHref Brandhuber A, Penante B, Travaglini G et al. (2014). The last of the simple remainders. nameOfConference DOI: 10.1007/JHEP08(2014)100 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/7646 Penante B, Spence B, Travaglini G et al. (2014). On super form factors of half-BPS operators in N=4 super Yang-Mills. nameOfConference DOI: 10.1007/JHEP04(2014)083 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/7643 Huang YT, Wen C (2014). ABJM amplitudes and the positive orthogonal Grassmannian. nameOfConference DOI: 10.1007/JHEP02(2014)104 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/39664 Bianchi M, Brandhuber A, Travaglini G et al. (2014). Simplifying instanton corrections to N=4 SYM correlators. nameOfConference DOI: 10.1007/JHEP04(2014)101 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/7648 de Mello Koch R, Ramgoolam S, Wen C (2013). On the refined counting of graphs on surfaces. nameOfConference DOI: 10.1016/j.nuclphysb.2013.01.023 QMRO: qmroHref Brandhuber A, Travaglini G, Wen C (2012). All one-loop amplitudes in N=6 superconformal Chern-Simons theory. nameOfConference DOI: 10.1007/JHEP10(2012)145 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/4120 Nandan D, Wen C (2012). Generating all tree amplitudes in by Inverse Soft Limit. nameOfConference DOI: 10.1007/jhep08(2012)040 QMRO: qmroHref Brandhuber A, Travaglini G, Wen C (2012). A note on amplitudes in N=6 superconformal Chern-Simons theory. nameOfConference DOI: 10.1007/JHEP07(2012)160 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/3764 Nandan D, Volovich A, Wen C (2012). On Feynman rules for Mellin amplitudes in AdS/CFT. nameOfConference DOI: 10.1007/jhep05(2012)129 QMRO: qmroHref CAI B, WEN C, YANG H (2007). GLUEBALL MASSES FROM ADS6 GRAVITY THEORY. nameOfConference DOI: 10.1142/s0217732307023316 QMRO: qmroHref CHEN G, LUO M, WEN C (2007). LOOPS IN SUPER YANG-MILLS THEORIES. nameOfConference DOI: 10.1142/s0217732307023274 QMRO: qmroHref WEN C-K, YANG H-X (2005). QCD4 GLUEBALL MASSES FROM AdS6 BLACK HOLE DESCRIPTION. nameOfConference DOI: 10.1142/s0217732305016245 QMRO: qmroHref He S, Nandan D, Wen C (publicationYear). Note on bonus relations for supergravity tree amplitudes. nameOfConference DOI: 10.1007/jhep02(2011)005 QMRO: qmroHref Bourjaily JL, Trnka J, Volovich A et al. (2011). The Grassmannian and the twistor string: connecting all trees in SYM. nameOfConference DOI: 10.1007/jhep01(2011)038 QMRO: qmroHref Nandan D, Volovich A, Wen C (2010). A grassmannian étude in NMHV minors. nameOfConference DOI: 10.1007/jhep07(2010)061 QMRO: qmroHref Nguyen D, Spradlin M, Volovich A et al. (2010). The tree formula for MHV graviton amplitudes. nameOfConference DOI: 10.1007/jhep07(2010)045 QMRO: qmroHref Nguyen D, Spradlin M, Volovich A et al. (2010). The tree formula for MHV graviton amplitudes. nameOfConference DOI: 10.1007/jhep07(2010)045 QMRO: qmroHref Drummond JM, Spradlin M, Volovich A et al. (2009). Tree-level amplitudes in N=8 supergravity. nameOfConference DOI: 10.1103/physrevd.79.105018 QMRO: qmroHref Volovich A, Wen C (publicationYear). Correlation functions in non-relativistic holography. nameOfConference DOI: 10.1088/1126-6708/2009/05/087 QMRO: qmroHref Spradlin M, Volovich A, Wen C (2009). Three applications of a bonus relation for gravity amplitudes. nameOfConference DOI: 10.1016/j.physletb.2009.02.059 QMRO: qmroHref Spradlin M, Volovich A, Wen C (2008). Three-loop leading singularities and Bern-Dixon-Smirnov ansatz for five particles. nameOfConference DOI: 10.1103/physrevd.78.085025 QMRO: qmroHref Luo M, Wen C (2005). Compact formulas for tree amplitudes of six partons. nameOfConference DOI: 10.1103/physrevd.71.091501 QMRO: qmroHref Luo M, Wen C (publicationYear). Recursion relations for tree amplitudes in super gauge theories. nameOfConference DOI: 10.1088/1126-6708/2005/03/004 QMRO: qmroHref Luo M, Wen C (2005). Systematics of one-loop scattering amplitudes in N=4 super-Yang–Mills theories. nameOfConference DOI: 10.1016/j.physletb.2005.01.041 QMRO: qmroHref Luo MX, Wen CK (2005). Compact formulas for tree amplitudes of six partons. nameOfConference DOI: 10.1103/PhysRevC.71.091501 QMRO: qmroHref Luo M, Wen C (publicationYear). One-loop maximal helicity violating amplitudes in N = 4 super Yang-Mills theories. nameOfConference DOI: 10.1088/1126-6708/2004/11/004 QMRO: qmroHref SupervisionScattering amplitudes: New formulations and Applications Scattering amplitudes are one of the most fundamental observables in quantum field theory and string theory. In recent years, hidden structures of scattering amplitudes have been uncovered, and extremely powerful computational methods have been developed. These developments have dramatically improved our understanding of quantum field theory and string theory. This project will focus on the most recent and remarkable developments in this rapidly evolving research field. In particular, the research projects include new formulations of scattering amplitudes, as well as the applications of scattering amplitudes to other research areas ranging from constraining effective field theories to gravitational waves to holographic correlation functions in the context of AdS/CFT duality. Requirements: knowledge of Quantum Field Theory, String Theory and Supersymmetry at the level of a Master course.