arXiv subjects

Andreas Gustavsson

Publications and source records attributed to Andreas Gustavsson.

At least 37 records · Page 2Linked to original sources

arXiv2018

Superconformal indices on $S^1\times (S^5/Z_p)$

We obtain generating functions associated to the abelian superconformal indices for 6d $(1,0)$ tensor and hypermultiplets on $S^1\times (S^5/Z_p)$. We extract the superconformal indices and their high and low temperature behaviors. We consider round and generically squashed $S^5$ in turn. We show that the unsquashed limit of the superconformal indices is smooth. We examine S-duality in the large $p$ limit that acts by exchanging the Hopf circle with the temporal circle.

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arXiv2017

Five-dimensional fermionic Chern-Simons theory

We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d MSYM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.

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arXiv2017

Conformal Janus on Euclidean Sphere

We interpret Janus as an interface in a conformal field theory and study its properties. The Janus is created by an exactly marginal operator and we study its effect on the interface conformal field theory on the Janus. We do this by utilizing the AdS/CFT correspondence. We compute the interface free energy both from leading correction to the Euclidean action in the dual gravity description and from conformal perturbation theory in the conformal field theory. We find that the two results agree each other and that the interface free energy scales precisely as expected from the conformal invariance of the Janus interface.

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arXiv2016

Witten indices of abelian M5 brane on $\mathbb{R}\times S^5$

Witten indices and partition functions are computed for abelian 6d tensor and hypermultiplets on $\mathbb{R}\times S^5$ in Lorentzian signature in an R gauge field background which preserves some supersymmetry. We consider a generic supersymmetric squashing that also admits squashing of the Hopf fiber. Wick rotation to Euclidean M5 brane amounts to Wick rotation of squashing parameters and the hypermultiplet mass parameter. We compute Casimir energies for tensor and hypermultiplets separately for general squashing, and match these with the corresponding gravitational anomaly polynomials. We extract Witten indices on $\mathbb{R}\times \mathbb{CP}^2$ and find that this is zero, again matching with the vanishing anomaly polynomial on an odd dimensional space.

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arXiv2015

Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds

We obtain the action for a curved superconformal abelian M5 brane with the background R-symmetry gauge field turned on. We then restrict ourselves to superconformal M5 brane on a sphere times flat Minkowski space. We choose R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5 brane actions on $M_{1,1} \times S^4$ and $M_{1,2} \times S^3$ where actions and all fields, including the background gauge field, are real. Dimensional reduction along time gives real 5d SYM actions with nonabelian generalizations.

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arXiv2015

The geometric Langlands twist in five and six dimensions

Abelian 6d (2,0) theory has SO(5) R symmetry. We twist this theory by identifying the R symmetry group with the SO(5) subgroup of the SO(1,5) Lorentz group. This twisted theory can be put on any five-manifold M, times R, while preserving one scalar supercharge. We subsequently assume the existence of one unit normalized Killing vector field on M, and we find a corresponding SO(4) twist that preserves two supercharges and is a generalization of the geometric Langlands twist of 4d SYM. We generalize the story to non-Abelian gauge group for the corresponding 5d SYM theories on M. We derive a vanishing theorem for BPS contact instantons by identifying the 6d potential energy and its BPS bound, in the 5d theory. To this end we need to perform a Wick rotation that complexifies the gauge field.

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arXiv2015

Euclidean quantum M5 brane theory on $S^1 \times S^5$

We consider Euclidean quantum M5 brane theory on $S^1\times S^5$. Dimensional reduction along $S^1$ gives a 5d SYM on $S^5$. We derive this 5d SYM theory from a classical Lorentzian M5 brane Lagrangian on $S^1 \times S^5$, where $S^1$ is a timelike circle of radius $T$, by performing a Scherk-Schwarz reduction along $S^1$ followed by Wick rotation of $T$.

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arXiv2014

Elliptic genera of monopole strings

We obtain the elliptic genera of monopole strings in 5d MSYM. We find agreement with corresponding TST-dual dyonic-instanton single particle indices in 1110.2175. We make use of (2,2) superconformal algebra and its spectral flow, and the agreement can therefore be taken as evidence that monopole string (4,4) sigma models are exactly quantum superconformal.

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arXiv2013

One dyonic instanton in 5d maximal SYM theory

We study the one-instanton sector of 5d U(N) maximal SYM theory. By using the moduli space approximation we obtain all the 1/4-BPS bound states of one dyonic instanton when a vev is given to one of the SYM scalar fields that breaks U(N) maximally. We compute the corresponding 1/4-BPS index and partition function and find agreement with arXiv:1110.2175.

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arXiv2012

M5/D4 brane partition function on a circle bundle

We consider Abelian M5 brane on a six-manifold which we take as a circle bundle over a five-manifold $M$. We compute the zero mode part of the M5 brane partition function using Chern-Simons theory and Hamiltonian formulation respectively and find an agreement. We also show that the D4 brane on $M$ shares exactly the same zero mode partition function again using the Hamiltonian formulation. For the oscillator modes we find that KK modes associated with the circle compactification are missing from the D4 brane. By making an infinitesimal noncommutative deformation we have instanton threshold bound states. We explicitly compute the instanton partition function up to instanton charge three, and show a perfect match with a corresponding contribution inside the M5 brane partition function, thus providing a very strong supporting evidence that D4 brane is identical with M5 brane which extends beyond the BPS sector. We comment on the modular properties of the M5 brane partition function when compactified on $T^2$ times a four-manifold. We briefly discuss a case of a singular fibration.

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arXiv2012

Deconstructing graviphoton from mass-deformed ABJM

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two-sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is $U(N)\times U(N-1)$. We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang -Mills coupling constant to the value which corresponds to M5 brane compactified on $\mb{R}^ {1,2} \times S^3/{\mb{Z}_k}$. The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.

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arXiv2011

Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)

The ABJM theory refers to superconformal Chern-Simons-matter theory with product gauge group U(L)xU(R) and level +k, -k, respectively. The theory is a candidate for worldvolume dynamics of M2-branes sitting at C(4)/Z(k)k. By utilizing monopole operators, we prove that ABJM theory gets enhanced N=8 supersymmetry and SO(8) R-symmetry at Chern-Simons levels k=1,2. We first show that the ABJM Lagrangian can be written in a manifestly SO(8) invariant form up to certain extra terms. We then show that upon integrating out Chern-Simons gauge fields these extra terms vanish precisely at levels k=1,2. Utilizing monopole operators at these levels, we identify new N=2 supersymmetry. We demonstrate that they combine with the manifest N=6 supersymmetry to close on-shell on N=8 supersymmetry. We finally show that the ABJM scalar potential is SO(8) invariant.

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arXiv2011

M5 brane on $R^{1,2} \times S^3$

We deconstruct 16 rigid supersymmetry variations for M5 brane on $\mb{R}^{1,2}\times (S^3/{\mb{Z}_k})$ and obtain on-shell closure on Lie derivatives. Dimensional reduction on the Hopf fiber by taking $k\rightarrow \infty$ gives sYM on ${\mb{R}}^{1,2} \times S^2$ with 8 rigid supersymmetries. We reproduce the result in arXiv:0908.3263 but we also derive an additional graviphoton term which is associated with the twisting of the Hopf bundle.

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arXiv2011

A preliminary test of Abelian D4-M5 duality

We compute the partition function of five-dimension Abelian sYM including a graviphoton term on a five-torus. The result agrees with Abelian M5 brane partition function with zero characteristics on an associated six-torus.

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arXiv2011

Five-dimensional SYM from undeformed ABJM

We expand undeformed ABJM theory around the vacuum solution that was found in arxiv:0909.3101. This solution can be interpreted as a circle-bundle over a two-dimensional plane with a singularity at the origin. By imposing periodic boundary conditions locally far away from the singularity, we obtain a local fuzzy two-torus over which we have a circle fibration. By performing fluctuation analysis we obtain five-dimensional SYM with the precise value on the coupling constant that we would obtain by compactifying multiple M5 branes on the vacuum three-manifold. In the resulting SYM theory we also find a coupling to a background two-form.

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arXiv2011

Five-dimensional super Yang-Mills theory from ABJM theory

We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the Yang-Mills coupling constant $g_{YM}^2 = 4π^2 R/K$. If we consider $S^3/{\mb{Z}_K}$ as a fiber bundle over $S^2$ then $R/K$ is the circumference of the fiber. The value on the coupling constant agrees with what one gets by compactifying M five-brane on that fiber. For this computation we take $R,K\to \infty$ while keeping $R/K$ at a fixed finite value. We also study mass deformed star-three-product BLG theory at K=1 and $R\to \infty$. In that limit we obtain Lorentz covariant supersymmetry variations and gauge variations of a non-Abelian tensor multiplet.

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arXiv2010

Monopoles, three-algebras and ABJM theories with $\N=5,6,8$ supersymmetry

We extend the hermitian three-algebra formulation of ABJM theory to include $U(1)$ factors. With attention payed to extra $U(1)$ factors, we refine the classification of $\N=6$ ABJM theories. We argue that essentially the only allowed gauge groups are $SU(N)\times SU(N)$, $U(N)\times U(M)$ and $Sp(N)\times U(1)$ and that we have only one independent Chern-Simons level in all these cases. Our argument is based on integrality of the $U(1)$ Chern-Simons levels and supersymmetry. A relation between monopole operators and Wilson lines in Chern-Simons theory suggests certain gauge representations of the monopole operators. From this we classify cases where we can not expect enhanced $\N=8$ supersymmetry. We also show that there are two equivalent formulations of $\N=5$ ABJM theories, based on hermitian three-algebra and quaternionic three-algebra respectively. We suggest properties of monopoles in $\N=5$ theories and show how these monopoles may enhance supersymmetry from $\N=5$ to $\N=6$.

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arXiv2010

An associative star-three-product and applications to M two/M five-brane theory

The star-product between functions enable us to take the large $N$ limit in a controlled way. At finite $N$ it serves as a substitute for matrix multiplications. Non-abelian gauge theory can be deconstructed from lower dimensional gauge theories using star-products. In this paper we extend the star-product to a star-three-product. We then apply the star-three-product to realize hermitian three-algebra of ABJM theory. We define a fuzzy three-torus. We deconstruct Abelian M five-brane in a constant background three-form potential on a fuzzy three-torus. We deconstruct non-Abelian extensions which might be related with multiple M five branes. We also mention the fuzzy three-sphere case.

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