Outputs (29)

3d N = 4 Gauge Theories on an Elliptic Curve (2022)
Journal Article
Bullimore, M., & Zhang, D. (2022). 3d N = 4 Gauge Theories on an Elliptic Curve. SciPost Physics, 13(1), https://doi.org/10.21468/scipostphys.13.1.005

This paper studies 3d N = 4 supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection f... Read More about 3d N = 4 Gauge Theories on an Elliptic Curve.

The 3d twisted index and wall-crossing (2022)
Journal Article
Bullimore, M., Ferrari, A., & Kim, H. (2022). The 3d twisted index and wall-crossing. SciPost Physics, 12(6), Article 186. https://doi.org/10.21468/scipostphys.12.6.186

We study the twisted index of 3d N = 2 supersymmetric gauge theories on S 1 ×Σ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on S 1 . Using supersymmetr... Read More about The 3d twisted index and wall-crossing.

The twisted index and topological saddles (2022)
Journal Article
Bullimore, M., Ferrari, A. E., Kim, H., & Xu, G. (2022). The twisted index and topological saddles. Journal of High Energy Physics, 2022(5), Article 116. https://doi.org/10.1007/jhep05%282022%29116

The twisted index of 3d N = 2 gauge theories on S 1 × Σ has an algebrogeometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the supersymmetric quantum mechanics... Read More about The twisted index and topological saddles.

Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface (2022)
Journal Article
Bullimore, M., Ferrari, A., & Kim, H. (2022). Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface. SciPost Physics, 12(2), Article 072. https://doi.org/10.21468/scipostphys.12.2.072

This paper studies supersymmetric ground states of 3d N = 4 supersymmetric gauge theories on a Riemann surface of genus g . There are two distinct spaces of supersymmetric ground states arising from the A and B type twists on the Riemann surface, whi... Read More about Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface.

Boundaries, Vermas and factorisation (2021)
Journal Article
Bullimore, M., Crew, S., & Zhang, D. (2021). Boundaries, Vermas and factorisation. Journal of High Energy Physics, 2021(4), Article 263. https://doi.org/10.1007/jhep04%282021%29263

We revisit the factorisation of supersymmetric partition functions of 3d N = 4 gauge theories. The building blocks are hemisphere partition functions of a class of UV N = (2, 2) boundary conditions that mimic the presence of isolated vacua at infinit... Read More about Boundaries, Vermas and factorisation.

Secondary products in supersymmetric field theory (2020)
Journal Article
Beem, C., Ben-Zvi, D., Bullimore, M., Dimofte, T., & Neitzke, A. (2020). Secondary products in supersymmetric field theory. Annales Henri Poincaré, 21(4), 1235-1310. https://doi.org/10.1007/s00023-020-00888-3

The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater than one. In theories of cohomological type, these commut... Read More about Secondary products in supersymmetric field theory.

Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps (2019)
Journal Article
Bullimore, M., Ferrari, A., & Kim, H. (2019). Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps. Journal of High Energy Physics, 2019(7), Article 14. https://doi.org/10.1007/jhep07%282019%29014

We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S 1 × Σ where Σ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have isolated vacua under generic mass and F... Read More about Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps.

Vortices and Vermas (2018)
Journal Article
Bullimore, M., Dimofte, T., Gaiotto, D., Hilburn, J., & Kim, H. (2018). Vortices and Vermas. Advances in Theoretical and Mathematical Physics, 22(4), 803-917. https://doi.org/10.4310/atmp.2018.v22.n4.a1

In three-dimensional gauge theories, monopole operators create and destroy vortices. We explore this idea in the context of 3d N=4 gauge theories in the presence of an Ω-background. In this case, monopole operators generate a non-commutative algebra... Read More about Vortices and Vermas.

Twisted Hilbert spaces of 3d supersymmetric gauge theories (2018)
Journal Article
Bullimore, M., & Ferrari, A. (2018). Twisted Hilbert spaces of 3d supersymmetric gauge theories. Journal of High Energy Physics, 2018(08), Article 018. https://doi.org/10.1007/jhep08%282018%29018

We study aspects of 3d N=2 supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the line. We propose a constru... Read More about Twisted Hilbert spaces of 3d supersymmetric gauge theories.

Three-Dimensional N = 4 Gauge Theories in Omega Background (2018)
Conference Proceeding
Bullimore, M. (2018). Three-Dimensional N = 4 Gauge Theories in Omega Background. In A. Kashani-Poor, R. Minasian, N. Nekrasov, & B. Pioline (Eds.), String-Math 2016 : June 27-July 2, 2016, Collège de France, Paris, France (1-20)

We review the description of three-dimensional gauge theories with N = 4 supersymmetry in the presence of an omega background as an N = 4 supersymmetric quantum mechanics. We will focus throughout on a simple abelian example. The Hilbert space of sup... Read More about Three-Dimensional N = 4 Gauge Theories in Omega Background.

Expanding the Bethe/Gauge dictionary (2017)
Journal Article
Bullimore, M., Kim, H., & Lukowski, T. (2017). Expanding the Bethe/Gauge dictionary. Journal of High Energy Physics, 2017(11), Article 055. https://doi.org/10.1007/jhep11%282017%29055

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects... Read More about Expanding the Bethe/Gauge dictionary.

The Coulomb Branch of 3d N=4 Theories (2017)
Journal Article
Bullimore, M., Dimofte, T., & Gaiotto, D. (2017). The Coulomb Branch of 3d N=4 Theories. Communications in Mathematical Physics, 354(2), 671-751. https://doi.org/10.1007/s00220-017-2903-0

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on th... Read More about The Coulomb Branch of 3d N=4 Theories.

Refined 3d-3d correspondence (2017)
Journal Article
Alday, L. F., Genolini, P. B., Bullimore, M., & van Loon, M. (2017). Refined 3d-3d correspondence. Journal of High Energy Physics, 2017(4), Article 170. https://doi.org/10.1007/jhep04%282017%29170

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N =... Read More about Refined 3d-3d correspondence.

Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory (2016)
Journal Article
Bullimore, M., Dimofte, T., Gaiotto, D., Hilburn, J., & Kim, H. (2016). Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory. Journal of High Energy Physics, 2016(10), Article 108. https://doi.org/10.1007/jhep10%282016%29108

We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for qua... Read More about Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory.

Supersymmetric Casimir energy and the anomaly polynomial (2015)
Journal Article
Bobev, N., Bullimore, M., & Kim, H. (2015). Supersymmetric Casimir energy and the anomaly polynomial. Journal of High Energy Physics, 2015(09), Article 142. https://doi.org/10.1007/jhep09%282015%29142

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D−1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with... Read More about Supersymmetric Casimir energy and the anomaly polynomial.

Defects and quantum Seiberg-Witten geometry (2015)
Journal Article
Bullimore, M., Kim, H., & Koroteev, P. (2015). Defects and quantum Seiberg-Witten geometry. Journal of High Energy Physics, 2015(05), Article 095. https://doi.org/10.1007/jhep05%282015%29095

We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on ℝ4 × S 1 in the presence of codimension two defects. The codimension two defects can be described either as monodromy defects, or by coup... Read More about Defects and quantum Seiberg-Witten geometry.

The superconformal index of the (2,0) theory with defects (2015)
Journal Article
Bullimore, M., & Kim, H. (2015). The superconformal index of the (2,0) theory with defects. Journal of High Energy Physics, 2015(05), Article 048. https://doi.org/10.1007/jhep05%282015%29048

We compute the supersymmetric partition function of the six-dimensional (2, 0) theory of type A N −1 on S 1 × S 5 in the presence of both codimension two and codimension four defects. We concentrate on a limit of the partition function depending on a... Read More about The superconformal index of the (2,0) theory with defects.

Defect networks and supersymmetric loop operators (2015)
Journal Article
Bullimore, M. (2015). Defect networks and supersymmetric loop operators. Journal of High Energy Physics, 2015(2), Article 066. https://doi.org/10.1007/jhep02%282015%29066

We consider topological defect networks with junctions in A N − 1 Toda CFT and the connection to supersymmetric loop operators in N=2 theories of class S on a four-sphere. Correlation functions in the presence of topological defect networks are compu... Read More about Defect networks and supersymmetric loop operators.

Scattering Amplitudes and Wilson Loops in Twistor Space (2014)
Book
Bullimore, M. R. (2014). Scattering Amplitudes and Wilson Loops in Twistor Space. Springer Verlag. https://doi.org/10.1007/978-3-319-00909-4

The superconformal index and an elliptic algebra of surface defects (2014)
Journal Article
Bullimore, M., Fluder, M., Hollands, L., & Richmond, P. (2014). The superconformal index and an elliptic algebra of surface defects. Journal of High Energy Physics, 2014(10), Article 062. https://doi.org/10.1007/jhep10%282014%29062

In this paper we continue the study of the superconformal index of four-dimensional N =2 theories of class S in the presence of surface defects. Our main result is the construction of an algebra of difference operators, whose elements are labeled by... Read More about The superconformal index and an elliptic algebra of surface defects.

Surface defects, the superconformal index and q-deformed Yang-Mills (2013)
Journal Article
Alday, L. F., Bullimore, M., Fluder, M., & Hollands, L. (2013). Surface defects, the superconformal index and q-deformed Yang-Mills. Journal of High Energy Physics, 2013(10), Article 018. https://doi.org/10.1007/jhep10%282013%29018

Recently a prescription to compute the four-dimensional N = 2 superconformal index in the presence of certain BPS surface defects has been given. These surface defects are labelled by symmetric representations of SU(N). In the present paper we give a... Read More about Surface defects, the superconformal index and q-deformed Yang-Mills.

On S-duality of the superconformal index on lens spaces and 2d TQFT (2013)
Journal Article
Alday, L. F., Bullimore, M., & Fluder, M. (2013). On S-duality of the superconformal index on lens spaces and 2d TQFT. Journal of High Energy Physics, 2013(05), Article 122. https://doi.org/10.1007/jhep05%282013%29122

We consider the 4d superconformal index for N=2 gauge theories on S 1 × L(r, 1), where L(r, 1) is a Lens space. We focus on a one-parameter slice of the three-dimensional fugacity space and in that sector we show S-duality. We do so by rewriting the... Read More about On S-duality of the superconformal index on lens spaces and 2d TQFT.

Scattering amplitudes and Wilson loops in twistor space (2011)
Journal Article
Adamo, T., Bullimore, M., Mason, L., & Skinner, D. (2011). Scattering amplitudes and Wilson loops in twistor space. Journal of Physics A: Mathematical and Theoretical, 44(45), Article 454008. https://doi.org/10.1088/1751-8113/44/45/454008

This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for $\mathcal {N}=4$ super-Yang–Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally sup... Read More about Scattering amplitudes and Wilson loops in twistor space.

MHV diagrams from an all-loop recursion relation (2011)
Journal Article
Bullimore, M. (2011). MHV diagrams from an all-loop recursion relation. Journal of High Energy Physics, 2011(08), Article 107. https://doi.org/10.1007/jhep08%282011%29107

We derive an all-loop recursion relation for the rational integrands of scattering amplitudes in planar N=4 super Yang-Mills theory. The recursion relation is generated by an all-line shift of momentum twistors. We solve the recursion relation in det... Read More about MHV diagrams from an all-loop recursion relation.

A proof of the correlation function/supersymmetric Wilson loop correspondence (2011)
Journal Article
Adamo, T., Bullimore, M., Mason, L., & Skinner, D. (2011). A proof of the correlation function/supersymmetric Wilson loop correspondence. Journal of High Energy Physics, 2011(08), Article 076. https://doi.org/10.1007/jhep08%282011%29076

We prove that in the limit when its insertion points become pairwise null-separated, the ratio of certain n-point correlation functions in N=4 SYM is equal to a supersymmetric Wilson loop on twistor space, acting in the adjoint representation. In the... Read More about A proof of the correlation function/supersymmetric Wilson loop correspondence.

Inverse soft factors and grassmannian residues (2011)
Journal Article
Bullimore, M. (2011). Inverse soft factors and grassmannian residues. Journal of High Energy Physics, 2011(01), Article 055. https://doi.org/10.1007/jhep01%282011%29055

The action of holomorphic inverse soft factors on scattering amplitudes in N=4 SYM is shown to take a remarkably simple form in momentum twistor space. This is used to identify individual residues of the grassmannian with primitive leading singularit... Read More about Inverse soft factors and grassmannian residues.

MHV diagrams in momentum twistor space (2010)
Journal Article
Bullimore, M., Mason, L., & Skinner, D. (2010). MHV diagrams in momentum twistor space. Journal of High Energy Physics, 2010(12), Article 032. https://doi.org/10.1007/jhep12%282010%29032

We show that there are remarkable simplifications when the MHV diagram formalism for N=4 super Yang-Mills is reformulated in momentum twistor space. The vertices are replaced by unity while each propagator becomes a dual superconformal ‘R-invariant’... Read More about MHV diagrams in momentum twistor space.

Kinetic mixing of U(1)’s for local string models (2010)
Journal Article
Bullimore, M., Conlon, J. P., & Witkowski, L. T. (2010). Kinetic mixing of U(1)’s for local string models. Journal of High Energy Physics, 2010(11), Article 142. https://doi.org/10.1007/jhep11%282010%29142

We study kinetic mixing between massless U(1)s in toroidal orbifolds with D3-branes at orbifold singularities. We focus in particular on C3/Z4 singularities but also study C3/Z6 and C3/Z′6 singularities. We find kinetic mixing can be present and desc... Read More about Kinetic mixing of U(1)’s for local string models.

Twistor-strings, Grassmannians and leading singularities (2010)
Journal Article
Bullimore, M., Mason, L., & Skinner, D. (2010). Twistor-strings, Grassmannians and leading singularities. Journal of High Energy Physics, 2010(03), Article 070. https://doi.org/10.1007/jhep03%282010%29070

We derive a systematic procedure for obtaining explicit, ℓ-loop leading singularities of planar N = 4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagram. The expressions are given as integrals o... Read More about Twistor-strings, Grassmannians and leading singularities.