arXiv subjects

D. D. Tolla

Publications and source records attributed to D. D. Tolla.

At least 19 recordsLinked to original sources

arXiv2023

Spontaneous Supersymmetry Breaking in Inhomogeneous Supersymmetric Field Theories and BPS Vacua

We study spontaneous supersymmetry breaking in inhomogeneous extensions of ${\cal N}=1$ supersymmetric field theory models in 4-dimensions. The ${\cal N}=1$ Abelian Higgs model with the inhomogeneous mass parameter and the FI coefficient that are dependent on spatial coordinates, as well as the O'Raifeartaigh model with all its parameters being dependent on spatial coordinates, are studied in detail. In the presence of inhomogeneous parameters, half supersymmetry can be preserved by adding appropriate inhomogeneous deformations to the original Lagrangians. The inhomogeneous deformations often break the R-symmetry explicitly. In cases where the inhomogeneous deformations do not break the R-symmetry explicitly, we demonstrate that spontaneous breaking of the R-symmetry is infeasible. We argue that those models can not be spontaneous supersymmetry breaking models, according to the Nelson-Seiberg argument. We comment on this issue in the context of a generic ${\cal N}=1$ supersymmetric model as well.

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arXiv2020

Super Yang-Mills Theories with Inhomogeneous Mass Deformations

We construct the 4-dimensional ${\cal N}=\frac12$ and ${\cal N}=1$ inhomogeneously mass-deformed super Yang-Mills theories from the ${\cal N} =1^*$ and ${\cal N} =2^*$ theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the ${\cal N} =4$ super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $ {\cal N}=\frac12$ theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

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arXiv2020

Renormalized Holographic Subregion Complexity under Relevant Perturbations

We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and AdS$_5$ geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the $d=3$ and $d=4$ dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS$_5$ geometry under relevant perturbations with operators of conformal dimensions in the range $0< Δ< \frac{1}{2}\,\, {\rm and} \,\, \frac{7}{2}< Δ< 4$ cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly.

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arXiv2019

Holography of Massive M2-brane Theory with Discrete Torsion

We investigate the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJ theory with U$_k(N+l)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)$\times$SO(4)/${\mathbb Z}_k\times$SO(4)/${\mathbb Z}_k$ isometry and the discrete torsion $l$. For chiral primary operators with conformal dimensions $Δ=1,2$, we obtain the exact vacuum expectation values using the holographic method in 11-dimensional supergravity and show that the results depend on the shapes of droplet pictures in LLM geometries. The $\frac{l}{\sqrt{N}}$ contributions from the discrete torsion $l$ for several simple droplet pictures in the large $N$ limit are determined in holographic vacuum expectation values. We also explore the effects of the orbifolding ${\mathbb Z}_k$ and the asymptotic discrete torsion $l$, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.

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arXiv2019

Gravitational Waves as a Probe of the Extra Dimension

We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification radius, the 4- dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor and one KK scalar modes after a gauge fixing. We treat those massive KK modes as stochastic sources of gravitational wave (GW) with characteristic dependences of the frequencies on the size of the extra dimension. Using the observational bounds on the size of the extra dimension and on the characteristic strain, we make an order estimation on the frequencies and amplitudes of the massive KK modes that can contribute to the GW.

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arXiv2018

Gravity from Entanglement and RG Flow in a Top-down Approach

The duality between a $d$-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS$_{d+1}$ geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS$_4$ gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS$_4$ metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

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arXiv2018

Holography of Massive M2-brane Theory: Non-linear Extension

We investigate the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)$\times$SO(4)/${\mathbb Z}_k$ $\times$SO(4)/${\mathbb Z}_k$ isometry, in terms of a KK holography, which involves quadratic order field redefinitions. As a non-trivial extension of the previous work arXiv:1612.05066, we implement the KK mappings for various gauge invariant fields up to quadratic order to obtain 4-dimensional gravity fields. The non-linearity of the KK maps indicates that, in the current case, we can observe the true purpose of the non-linear KK holography of the LLM solutions. Using such KK holography procedure, we obtain the vacuum expectation values of the chiral primary operator of conformal dimension $Δ= 2$ in the large $N$ limit but with general $k$ and examine the gauge/gravity duality for LLM solutions, which are represented by square-shaped Young diagrams. We also show that the vacuum expectation values of the massive KK graviton modes are vanishing as expected by the supersymmetry.

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arXiv2017

Mass-deformed ABJM Theory and LLM Geometries: Exact Holography

We present a detailed account and extension of our claim in arXiv:1610.01490. We test the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)/${\mathbb Z}_k$ $\times$SO(4)/${\mathbb Z}_k$ isometry, in the large $N$ limit. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein holography to the LLM geometries. We focus on the chiral primary operator with conformal dimension $Δ= 1$. We show that $\langle {\cal O}^{(Δ=1)}\rangle= N^{\frac32} \, f_{(Δ=1)}$ for all supersymmetric vacuum solutions and LLM geometries with $k=1$, where the factor $f_{(Δ)}$ is independent of $N$. We also confirm that the vacuum expectation value of the the energy momentum tensor is vanishing as expected by the supersymmetry. We extend our results to the case of $k\ne 1$ for LLM geometries represented by rectangular-shaped Young-diagrams. In analogy with the Coulomb branch of the ${\cal N} = 4$ super Yang-Mills theory, we argue that the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM geometries are parametrized by the vevs of the chiral primary operators.

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arXiv2017

Exact Holography of the Mass-deformed M2-brane Theory

We test the holographic relation between the vacuum expectation values of gauge invariant operators in ${\cal N} = 6$ ${\rm U}_k(N)\times {\rm U}_{-k}(N)$ mass-deformed ABJM theory and the LLM geometries with $\mathbb{Z}_k$ orbifold in 11-dimensional supergravity. To do that, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension $Δ= 1$, which is given by $\langle {\cal O}^{(Δ=1)}\rangle= N^{\frac32} \, f_{(Δ=1)}$, for large $N$ and $k=1$. Here factor $f_{(Δ)}$ is independent of $N$. Our results involve infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a nontrivial test of gauge/gravity duality away from the conformal fixed point. We also extend our results to the case of $k\ne 1$ for LLM geometries represented by rectangular-shaped Young-diagrams.

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arXiv2015

Abelian Gauge Invariance of the WZ-type Coupling in ABJM Theory

We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously invariant under the U$_{\textrm{L}}(N)\times$U$_{\textrm{R}}(N)$ non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.

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arXiv2013

The energy of the analytic lump solution in SFT

In a previous paper a method was proposed to find exact analytic solutions of open string field theory describing lower dimensional lumps, by incorporating in string field theory an exact renormalization group flow generated by a relevant operator in a worldsheet CFT. In this paper we compute the energy of one such solution, which is expected to represent a D24 brane. We show, both numerically and analytically, that its value corresponds to the theoretically expected one.

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arXiv2013

Abelian Projections of the Mass-deformed ABJM theory and Weakly Curved Dual Geometry

We construct ${\cal N}=2,4$ supersymmetric abelian projections of the ${\cal N}=6$ mass-deformed ABJM theory. There are well-defined dual background geometries for the ${\cal N}=2$ abelian theory, while those geometries are unclear for the ${\cal N}=4$ abelian theory. The ${\cal N}=2$ theory is built on the supersymmetric vacua of the mass-deformed ABJM theory, which are proven to have one-to-one correspondence with the ${\mathbb Z}_k$ quotient of Lin-Lunin-Maldacena geometries. We select one special vacuum of the mass-deformed ABJM theory and show that the corresponding geometry is weakly curved at every point of the entire space transverse to the M2-branes in the large $N$ limit.

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arXiv2012

Partially Supersymmetric ABJM Theory with Flux

Starting with generic Wess-Zumino type coupling to constant four-form and the dual seven-form field strengths in the ABJM theory, we obtain mass-deformed theories with ${\cal N}=2,4$ supersymmetries. These theories contain massless scalar fields and allow the implementation of the Mukhi-Papageorgakis Higgsing procedure. Using this procedure, we connect the Higgsed theories to three-dimensional mass-deformed SYM theories. These are also connected by the four-dimensional ${\cal N}=1^*,2^*$ mass-deformed SYM theories through dimensional reduction. We classify the three-dimensional mass-deformed SYM theories of ${\cal N}=1,2,4$ supersymmetry, of which a few cases of ${\cal N}=1,2$ are connected neither by MP Higgsing procedure nor dimensional reduction.

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arXiv2012

Lump solutions in SFT. Complements

Recently a possible violation of the equation of motion for the recently proposed lump solutions in open SFT has been pointed out in the literature. In this paper we argue that, when the issue is considered in the appropriate mathematical setting of distribution theory, no violations to the equation of motion occur.

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arXiv2011

${\cal N}=3$ Supersymmetric Effective Action of D2-branes in Massive IIA String Theory

We obtain a new-type of ${\cal N}=3$ Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgsing of the ${\cal N}=3$ Gaiotto-Tomasiello theory. This theory has ${\cal N}=1$ BPS fuzzy funnel solution which is expressed in terms of the seven generators of SU(3), excluding $T_8$. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.

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arXiv2011

Relevant Deformations in Open String Field Theory: a Simple Solution for Lumps

We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two--dimensional world-sheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.

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arXiv2011

On the Vacua of Mass-deformed Gaiotto-Tomasiello Theories

We write explicit Lagrangian and supersymmetry transformation rules using the component fields in the ${\cal N}=2,3$ GT theories. In the component field expansion, the manifestation of an additional ${\cal N}=1$ supersymmetry is verified in the ${\cal N}=3$ GT theory. We find maximal supersymmetry preserving mass-deformation of the GT theories and their classical supersymmetric discrete vacua. Some interesting aspects of the set of discrete vacua are discussed in comparison with the ABJM case.

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arXiv2011

Mass-Deformed Super Yang-Mills Theories from M2-Branes with Flux

We consider $(2+1)$-dimensional mass-deformed SYM theories and their M-theory origin. These are obtained from MP Higgsing of ABJM theory with constant flux and fixing the mass terms via supersymmetry completion. Depending on the choice of the flux, we obtain ${\cal N}=1$, ${\cal N}=2$, and ${\cal N}=4$ mass-deformed SYM theories. For each of these cases we solve the vacuum equation and obtain the fuzzy two sphere solution for the first two cases. We also discuss the D-brane interpretation of the obtained mass-deformed SYM theories.

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