# Dr Sanjaye Ramgoolam

## Reader in Theoretical Physics

Email: s.ramgoolam@qmul.ac.uk

Telephone: 020 7882 5799

Room Number: G. O. Jones Building, Room 609

## Profile

My research is in the areas of string theory, combinatorics and representation theory. My papers are available at Google Scholar

I am currently teaching Mathematical Techniques 4 (Year 3) and Advanced Quantum Field theory (Year 4)

## Teaching

Currently teaching :

- PHY6324 (Mathematical Techniques 4)
- SPA7001U/P (Advanced Quantum Field Theory)

Undergraduate Projects supervised :

- From classical strings to photons and gravtions
- Plasma Physics and Nuclear Fusion
- Dark Matter, dark energy and cosmology
- Entanglement and decoherence in quantum physics

Modules taught in the past :

- Electromagnetic theory (4th year MSci course)
- Quantum Mechanics and Symmetry (3rd year)
- Electromagnetism for pre-medical (at Brown)
- Quantum Physics (1st year)

## Research

### Research Interests:

### String theory, representation theory, combinatorics

A primary area of focus in my research is gauge-string duality, in particular the AdS/CFT correspondence, which relates 4-dimensional quantum field theory (QFT) to 10-dimensional string theory. I have developed a mathematical framework based on representation theory and combinatorics for understanding the map between states in the QFT and states of strings, branes and geometries in the 10 dimensions. The mathematical framework has been used to develop holographic perspectives on tensor models. A recent theme emerging from these investigations is the role of two-dimensional topological field theories (TFT2) as a structure which captures both the combinatorics and spacetime dependences of correlators in four-dimensional theories. My latest paper on this theme defines diagram algebras which give mathematical meaning to tensorial calculus in general dimensions used in the dimensional regularization technique of quantum field theory. Links to a selection of papers are given below.

A very recent interdisciplinary direction (initiated in a collaboration with D. Kartsaklis and M. Sadrzadeh) has been to develop matrix theory techniques to give a framework for analyzing matrix data in computational linguistics. I am also interested in wider applications of random matrix theory ideas to data.

A complete list of my papers can be accessed at Inspire-HEP-database or Google scholar (Following standard practice in theoretical particle physics, author lists are all alphabetical)

Selected papers organised by theme (although some lie at interfaces of these themes**)**

**Tensor Models **

** **1. Tensor models and branched covers.

** **2. Tensor models, Kronecker coefficients and permutation algebras.

**CFT4 as TFT2**

1. CFT4 as SO(4,2)-invariant TFT2

3. Polynomial rings and CFT primary fields

4. Perturbative CFTs and diagram algebras

**Physics of Language **

2. Permutation Invariant Gaussian Matrix Models (PIGMM)

3. PIGMM meet data. (a talk on this at conference QPL2020)

#### AdS/CFT, giant graviton branes, correlators of gauge invariant operators

Half-BPS case (related to one-matrix combinatorics)

Eighth-BPS case (related to multi-matrix combinatorics)

- Diagonal multi-matrix correlators and BPS operators in N=4 SYM.
- From counting to construction of BPS states in N=4 SYM.
- Branes, anti-branes and brauer algebras in gauge-gravity duality.

#### Non-BPS and Integrability

#### Fuzzy geometry

- On spherical harmonics for fuzzy spheres in diverse dimensions.
- The Fuzzy S2 structure of M2-M5 systems in ABJM membrane theories.
- Noncommutative gravity from the AdS / CFT correspondence.
- Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons.

#### Mathematical models of gauge-string duality

- Large N 2-D Yang-Mills theory and topological string theory
- From Matrix Models and Quantum Fields to Hurwitz Space and the absolute Galois Group.
- Strings from Feynman Graph counting : without large N.

#### Supersymmetric Gauge theories

#### Matrix Model of M-theory

### Examples of research funding:

Current and recent grants (PI or CoI)

- Visiting Professorship, Wits University South Africa
- Science and Technology Facilities Council (£ 890,210) Consolidated Grant String Theory ``Amplitudes,Strings and Duality,'' (2020-2023)
- Science and Technology Facilities Council, (£703,989). Brandhuber, Berman, Buican, Figueras, Ramgoolam, Russo, Shigemori, Spence, Thomas, Travaglini, White. Consolidated grant String theory, gauge theory and duality (2017-2020)
- Science and Technology Facilities Council, (£632,431). Brandhuber, Berman, Ramgoolam, Russo, Spence, Thomas, Travaglini, Wecht. Consolidated grant String theory, gauge theory and duality (2011-2014)
- Workshop on ``Permutations and gauge-string duality,'' (July 2014) funded by STFC and European Science Foundation Activity ``holography and strongly coupled systems'' and South African National Research Foundation.
- Science and Technology Facilities Council, (£1,431,413). Spence Berman, Brandhuber, Ramgoolam, Russo, Thomas, Travaglini. Rolling grant String theory, gauge theory and duality (2008-2013)
- Particle Physics and Astronomy Research Council: Spence , Berman, Brandhuber, Ramgoolam, Thomas. Rolling grant String theory, gauge theory and gravity (2006-2010), (£249,800.)
- STFC (PPARC) Advanced Fellowship, 2003-2008 (£220,000)
- Scientist in charge for Marie Cure Outgoing Fellowship ( MOIF-CT-2006-038381) held by Diego Rodriguez Gomez at QMUL and Princeton.
- Royal Society International exchange grants with South Africa and Cyprus.

## Publications

The complete and up-to-date list of my publications is available at the Inspire-Hep database and at Google Scholar

A description of some my research organized according to some general themes is under the Research tab.

- Barnes G, Padellaro A, Ramgoolam S (2022),
**Permutation invariant Gaussian two-matrix models**$nameOfConference

- de Mello Koch R, He YH, Kemp G et al. (2022),
**Integrality, duality and finiteness in combinatoric topological strings**$nameOfConference

- Lewis-Brown C, Ramgoolam S (2021),
**Quarter-BPS states, multi-symmetric functions and set partitions**$nameOfConference

- de Mello Koch R, Ramgoolam S (2020),
**Perturbative 4D conformal field theories and representation theory of diagram algebras**$nameOfConference

- Ramgoolam S, Wilson MC, Zahabi A (2020),
**Quiver asymptotics: N=1 free chiral ring**$nameOfConference

- Kemp G, Ramgoolam S (2020),
**BPS states, conserved charges and centres of symmetric group algebras**$nameOfConference

- Ramgoolam S (2019),
**Permutation invariant Gaussian matrix models**$nameOfConference

- Kartsaklis D, Ramgoolam S, Sadrzadeh M (2019),
**Linguistic matrix theory**$nameOfConferenceDOI:**10.4171/aihpd/75**

- Ramgoolam S, Sedlak M (2019),
**Quantum information processing and composite quantum fields**$nameOfConference

- Lewis-Brown C, Ramgoolam S (2018),
**BPS operators in N=4 SO(N) super Yang-Mills theory: plethysms, dominoes and words**$nameOfConference

- Koch RDM, Ramgoolam S (2018),
**Free field primaries in general dimensions: counting and construction with rings and modules**$nameOfConference

- Geloun JB, Ramgoolam S (2017),
**Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras**$nameOfConference

- Koch RDM, Rabambi P, Rabe R et al. (2017),
**Free quantum fields in 4D and Calabi-Yau spaces**$nameOfConference

- Koch RDM, Rabambi P, Rabe R et al. (2017),
**Counting and construction of holomorphic primary fields in free CFT4 from rings of functions on Calabi-Yau orbifolds**$nameOfConference

- Kimura Y, Ramgoolam S, Suzuki R (2016),
**Flavour singlets in gauge theory as permutations**$nameOfConference

- Ramgoolam S (2016),
**Permutations and the combinatorics of gauge invariants for general $N$**$nameOfConferenceDOI:**10.22323/1.263.0107**

- Hanany A, Ramgoolam S, Rodriguez-Gomez D (publicationYear),
**Highest Weight Generating functions for hyperKahler T*(G/H) spaces**$nameOfConference

- Mattioli P, Ramgoolam S (2016),
**Gauge invariants and correlators in flavoured quiver gauge theories**$nameOfConference

- Hanany A, Jejjala V, Ramgoolam S et al. (2016),
**Consistency and derangements in brane tilings**$nameOfConference

- de Mello Koch R, Ramgoolam S (2016),
**Interactions as intertwiners in 4D QFT**$nameOfConference

- Mattioli P, Ramgoolam S (2016),
**Permutation Centralizer Algebras and Multi-Matrix Invariants**$nameOfConference

- Garner D, Ramgoolam S (2015),
**The geometry of the light-cone cell decomposition of moduli space**$nameOfConferenceDOI:**10.1063/1.4934365**

- Freidel L, Garner D, Ramgoolam S (2015),
**Permutation combinatorics of worldsheet moduli space**$nameOfConference

- Mattioli P, Ramgoolam S (2015),
**Quivers, words and fundamentals**$nameOfConference

- Koch RDM, Ramgoolam S (publicationYear),
**CFT4 as SO(4,2)-invariant TFT2**$nameOfConference

- Garner D, Ramgoolam S, Wen C (publicationYear),
**Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5**$nameOfConference

- Geloun JB, Ramgoolam S (2014),
**Counting Tensor Model Observables and Branched Covers of the 2-Sphere**$nameOfConferenceDOI:**10.4171/aihpd/4**

- Garner D, Ramgoolam S (2013),
**Holographic hierarchy in the Gaussian matrix model via the fuzzy sphere**$nameOfConference

- de Mello Koch R, Ramgoolam S, Wen C (2013),
**On the refined counting of graphs on surfaces**$nameOfConference

- Pasukonis J, Ramgoolam S (2013),
**Quivers as Calculators: Counting, Correlators and Riemann Surfaces**$nameOfConference

- de Mello Koch R, Ramgoolam S (2012),
**A double coset ansatz for integrability in AdS/CFT**$nameOfConference

- Pasukonis J, Ramgoolam S (2012),
**Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons**$nameOfConference

- de Mello Koch R, Ramgoolam S (2012),
**Strings from Feynman graph counting: Without large N**$nameOfConference

- Hanany A, He Y-H, Jejjala V et al. (2012),
**INVARIANTS OF TORIC SEIBERG DUALITY**$nameOfConference

- Hanany A, He YH, Jejjala V et al. (2012),
**Invariants of toric seiberg duality**$nameOfConference

- Hanany A, Jejjala V, Ramgoolam S et al. (2011),
**Calabi-Yau orbifolds and torus coverings**$nameOfConference

- Hanany A, Jejjala V, Ramgoolam S et al. (2011),
**Calabi-Yau orbifolds and torus coverings**$nameOfConference

- Jejjala V, Ramgoolam S, Rodriguez-Gomez D (2011),
**Toric CFTs, permutation triples, and Belyi pairs**$nameOfConference

- Pasukonis J, Ramgoolam S (2011),
**From counting to construction of BPS states in SYM**$nameOfConference

- Hanany A, He YH, Jejjala V et al. (2011),
**The beta ansatz: A tale of two complex structures**$nameOfConference

- Kimura Y, Ramgoolam S, Turton D (2010),
**Free particles from Brauer algebras in complex matrix models**$nameOfConference

- Nastase H, Papageorgakis C, Ramgoolam S (2009),
**The fuzzy S-2 structure of M2-M5 systems in ABJM membrane theories**$nameOfConference

- Brown TW, Heslop PJ, Ramgoolam S (2009),
**Diagonal free field matrix correlators, global symmetries and giant gravitons**$nameOfConference

- Kimura Y, Ramgoolam S (2008),
**Enhanced symmetries of gauge theory and resolving the spectrum of local operators**$nameOfConference

- Kimura Y, Ramgoolam S (2008),
**Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills**$nameOfConference

- Brown TW, Heslop PJ, Ramgoolam S (2008),
**Diagonal multi-matrix correlators and BPS operators in N=4 SYM**$nameOfConference

- Ramgoolam S (2008),
**Schur-Weyl duality as an instrument of gauge-string duality**$nameOfConferenceDOI:**10.1063/1.2972012**

- Kimura Y, Ramgoolam S (2007),
**Branes, anti-branes and Brauer algebras in gauge-gravity duality**$nameOfConference

- de Haro S, Ramgoolam S, Torrielli A (2007),
**Large N expansion of q-deformed two-dimensional Yang-Mills theory and Hecke algebras**$nameOfConference

- Brown T, Ramgoolam S, Koch RD et al. (2007),
**Correlators, probabilities and topologies in N=4 SYM**$nameOfConference

- Papageorgakis C, Ramgoolam S (2006),
**On time-dependent collapsing branes and fuzzy odd-dimensional spheres**$nameOfConference

- McNamara S, Papageorgakis C, Ramgoolam S et al. (2006),
**Finite N effects on the collapse of fuzzy spheres**$nameOfConference

- Papageorgakis C, Ramgoolam S, Toumbas N (2006),
**Noncommutative geometry, quantum effects and DBI-scaling in the collapse of D0-D2 bound states**$nameOfConference

- Koch RD, Jevicki A, Ramgoolam S (2005),
**On exponential corrections to the 1/N expansion in two-dimensional Yang Mills**$nameOfConference

- de Medeiros P, Ramgoolam S (2005),
**Non-associative gauge theory and higher spin interactions**$nameOfConference

- RAMGOOLAM SK, Papageorgakis C (2005),
**Large-small dualities between periodic collapsing/expanding branes and brane funnels**$nameOfConference

- Ramgoolam S, Spence B, Thomas S (2004),
**Resolving brane collapse with 1/N corrections in non-Abelian DBI**$nameOfConference

- Ramgoolam S (2004),
**Towards gauge theory for a class of commutative and non-associative fuzzy spaces**$nameOfConference

- Corley S, Ramgoolam S (2004),
**Strings on plane waves, super-Yang-Mills in four dimensions, quantum groups at roots of one**$nameOfConference

- THOMAS S, Ramgoolam S, Spence B (2004),
**Resolving brane collapse with 1/N corrections in non-Abelian DBI**$nameOfConference - Lowe DA, Nastase H, Ramgoolam S (2003),
**Massive IIA string theory and Matrix theory compactification**$nameOfConference

- Corley S, Ramgoolam S (2002),
**Finite factorization equations and sum rules for BPS correlators in N=4 SYM theory**$nameOfConference

- Ramgoolam S (2002),
**Higher dimensional geometries related to fuzzy odd-dimensional spheres**$nameOfConference

- Ho PM, Ramgoolam S (2002),
**Higher-dimensional geometries from matrix brane constructions**$nameOfConference

- Corley S, Lowe DA, Ramgoolam S (2001),
**Einstein-Hilbert on the brane**$nameOfConference - Ramgoolam S (2001),
**On spherical harmonics for fuzzy spheres in diverse dimensions**$nameOfConference

- Corley S, Lowe DA, Ramgoolam S (2001),
**Einstein-Hilbert action on the brane for the bulk graviton**$nameOfConference

- RAMGOOLAM SK, Jevicki A, Corley S (2001),
**Exact correlators of giant gravitons from dual N=4 SYM theory**$nameOfConference

- Corley S, Ramgoolam S (2001),
**Projector equivalences in K theory and families of non-commutative solitons**$nameOfConference

- Guralnik Z, Ramgoolam S (2001),
**On the polarization of unstable D0-branes into non-commutative odd spheres**$nameOfConference

- Mihailescu M, Ramgoolam S (2000),
**Duality and combinatorics of long strings in ADS3**$nameOfConference

- Jevicki A, Mihailescu M, Ramgoolam S (2000),
**Non-commutative spheres and the AdS/CFT correspondence**$nameOfConference

- Ramgoolam S (2000),
**A remark on T-duality and quantum volumes of zero-brane moduli spaces**$nameOfConference

- Jevicki A, Mihailescu M, Ramgoolam S (2000),
**Gravity from CFT on SN(X) : symmetries and interactions**$nameOfConference

- Ho P-M, Ramgoolam S, Tatar R (2000),
**Quantum space-times and finite N effects in 4D super Yang–Mills theories**$nameOfConference

- Jevicki A, Ramgoolam S (1999),
**Non commutative gravity from the ADS/CFT correspondence**$nameOfConference

- Ramgoolam S, Waldram D (1998),
**Zero branes on a compact orbifold**$nameOfConference

- Guralnik Z, Ramgoolam S (1998),
**From 0-branes to torons**$nameOfConference

- Brodie J, Ramgoolam S (1998),
**On matrix models of M5 branes**$nameOfConference

- Gopakumar R, Ramgoolam S (1998),
**Scattering of zero-branes off elementary strings in Matrix theory**$nameOfConference

- Ganor OJ, Gopakumar R, Ramgoolam S (1998),
**Higher loop effects in M(atrix) orbifolds**$nameOfConference

- Guralnik Z, Ramgoolam S (1997),
**Torons and D-brane bound states**$nameOfConference

- Ganor O (1997),
**Branes, fluxes and duality in M(atrix)-theory**$nameOfConference

- Cordes S, Moore G, Ramgoolam S (1997),
**Large N 2D Yang-Mills Theory and Topological String Theory**$nameOfConference

- Barbón JLF, Ramgoolam S (1997),
**Some properties of unstable monopoles in super-QCD**$nameOfConference

- Ramgoolam S, Thorlacius L (1997),
**D-branes and physical states**$nameOfConference

- RAMGOOLAM S (1996),
**WILSON LOOPS IN 2D YANG-MILLS: EULER CHARACTERS AND LOOP EQUATIONS**$nameOfConference

- Cordes S, Moore G, Ramgoolam S (1995),
**Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories**$nameOfConference

- Ramgoolam S (1994),
**Comment on two-dimensional O(N) and Sp(N) Yang-Mills theories as string theories**$nameOfConference

- Moore G, Plesser MR, Ramgoolam S (1992),
**Exact S-matrix for two-dimensional string theory**$nameOfConference

## Supervision

### PhDs/Postdocs

PhD students supervised :

- Costis Papageorgakis
- Tom Brown
- David Turton
- Jurgis Pasukonis
- David Garner
- Paolo Mattioli
- Christopher Lewis-Brown (Current)
- George Barnes
- Adrian Padellaro

Recent post-doctoral collaborators at QMUL :

- Ali Zahabi
- Diego Rodriguez Gomez
- Vishnu Jejjala
- Yusuke Kimura
- Paul Heslop
- Congkao Wen

This is not an exhaustive list and I would be happy to discuss other project possibilities.

## Project Title

### Combinatorics and Representation Theory in CFT, ADS/CFT, matrix/tensor models.

Symmetric groups and their group algebras, along with concepts in representation theory including Schur-Weyl duality, have been applied to the study of half-BPS states in N=4 SYM theory, in particular to clarify the holographic map of the AdS/CFT correspondence. **For full details click **here

## Public Engagement

### Outreach

Some popular science talks/presentations

- Linguistic Matrix Theory Video.
- Holography, Information and Meaning: Hidden symmetries of Matrix Physics [PDF 3,276KB] - Ps Star talk, 02/2019
- Duality and Emergence in String theory, talk at the Mauritius Diaspora Conference 2018
- Symmetries and Surprises in String Theory (Talk for Psi Star QMUL, December 2013)
- What is String Theory ? (talk at Bryanston School, April 2012)
- Strings and hidden geometries (talk at Inauguration of School of Phys and Astro 2012)
- String Theory and Hidden dimensions of spacetime (talk for Waltham Forest Physics masterclass)
- From force and matter to strings( talk at Highgate school, 2003)
- Strings in the quantum world ( talk at Oxford, 2009 )
- Duality and the nature of quantum space-time : ( talk at Oxford,Jan 2009 )
- Space and Time, Light and Gravity in String Theory ( talk at PPARC 2006)

### Some research presentations

- Permutation centralizer?algebras, polynomial invariants and supersymmetric states [PDF 1,066KB](talk at conference on representation theory and physics, Leeds, July 2016)
- BPS states, permutations and information (talk at YITP Kyoto programme on string theory, condensed matter physics and quantum information, June 2016)
- Quantum Field thories (QFTs), quivers and word combinatorics [PDF 4,825KB] (talk at theory group, computer science, EECS, QMUL, Oct. 21, 2015)
- CFT4?(4D?conformal QFT) as TFT2( 2D topological field theory) [PDF 4,438KB] (talk at school of Maths, QMUL, Mar 2, 2015)
- Quiver gauge theory and TFT2s (2d topological field theories) [PDF 8,116KB] (talk at Quantum integrability workshop, Surrey, 08/2014)
- Quantum states to brane geometries via fuzzy moduli space [PDF 517KB] (talk at Oxford Maths Institute, 02/12)
- Permutations, strings and Feynman Graphs [PDF 631KB] ( talk at City Maths Dept, 11/2011)
- Strings, Permutations and Quantum Fields [PDF 476KB] (talk at Corfu2011 workshop on non-commutatve field theory and gravity)
- Symmetric groups and local operators in gauge theory [PDF 499KB] (talk at Lisbon 2011)
- From numbers to strings and branes [PDF 83KB] (talk at Galileo Galilei Institute 2011)
- Feynman Diagrams and Absolute Galois group [PDF 293KB] (talk at B(A)MC 2010)
- Matrix Models, Hurwitz spaces Galois Group [PDF 667KB](talk in Southampton Pure Maths group)
- Fuzzy geometry of membranes in M-theory [PDF 314KB] (talk at Imperial)

### Short review articles:

- Permutations and the combinatorics of gauge invariants for general N.
- Schur-Weyl duality and Gauge-string duality (Talk given at "Ten years of AdS/CFT in Argentina,2008)