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We study mass deformations of $$ \mathcal{N} $$
 = 4, d = 4 SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of $$ \mathcal{N} $$
 = 1∗ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve d = 3 conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using D = 5 theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve d = 3 superconformal symmetry we construct a rich set of Janus solutions of $$ \mathcal{N} $$
 = 4 SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with $$ \mathcal{N} $$
 = 4 SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric AdS4 × S1 × S5 solution of type IIB supergravity.

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Spatially modulated and supersymmetric mass deformations of $\mathcal{N}=4$ SYM

We construct holographic Janus solutions, which describe a conformal interface in the theory of M2-branes, in four-dimensional gauged supergravities using a perturbative method. In particular, we study three Einstein-scalar systems and their BPS equations, which are derived by Bobev, Pilch, and Warner (2014). The actions of our interest are all consistent truncations of \begin{document}$ D = 11 $\end{document} supergravity, chosen to be invariant under \begin{document}$ SO(4)\times SO(4) $\end{document} , \begin{document}$ SU(3)\times U(1)\times U(1) $\end{document} , and \begin{document}$ G_2 $\end{document} symmetry subgroups of \begin{document}$ SO(8) $\end{document} . The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.

Re-visiting supersymmetric Janus solutions: a perturbative construction

We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function $m(x)= m_0 \sin k x$ and its derivative $m'(x)$. As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons have lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.

/pdf/ads-q-soliton-and-inhomogeneously-mass-deformed-abjm-model-3vs470ojz0.pdf

AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model

We study dual geometries to a deformed ABJM model with spatially dependent source functions at finite temperature. These source functions are proportional to the mass function m(x) = m0 sin kx and its derivative m′(x). As dual geometries, we find hairy black branes and AdS solitons corresponding to deconfinement phase and confining phase of the dual field theory, respectively. It turns out that the hairy AdS solitons have lower free energy than the black branes when the Hawking temperature is smaller than the confining scale. Therefore the dual system undergoes the first order phase transition. Even though our study is limited to the so-called Q-lattice ansatz, the solution space contains a set of solutions dual to a supersymmetric mass deformation. As a physical quantity to probe the confining phase, we investigate the holographic entanglement entropy and discuss its behavior in terms of modulation effect.

/pdf/ads-q-soliton-and-inhomogeneously-mass-deformed-abjm-model-2399ds7ful.pdf

AdS Q-soliton and inhomogeneously mass-deformed ABJM model

In this paper we study the thermodynamics of black branes with a modulated complex scalar in the context of bulk and boundary theories. The modulation induces inhomogeneity to the dual field theory, anisotropic pressure, and brane charge to the bulk geometry. The first law of thermodynamics and the Smarr relation are obtained using the off-shell ADT and the reduced action formalisms. We discuss the prescription for the mass of black branes, which relies on relevant and marginal deformations in the dual field theory. One of the cases is the gravity dual to a ABJM model with a sinusoidal mass function depending on a spatial coordinate. This is the first study of the deformed ABJM model at finite temperature including bulk thermodynamics.

/pdf/thermodynamics-of-inhomogeneously-mass-deformed-abjm-model-1nyvcihjq1.pdf

Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy

We find a $(1+1)$-dimensional metric solution for a background hosting various supersymmetric field theories with a single non-chiral real supercharge. This supersymmetric background is globally hyperbolic even though it contains a naked null singularity. In this regard, we show that scalar wave propagation on the background is well-defined and so the curvature singularity is a {\it mild} one. Taking inspiration from our previous work, we relate the field theory on this curved background to some classes of $(1+1)$-dimensional inhomogeneous field theory in the supersymmetric setup. Utilizing our supersymmetric background, we elucidate the limitations of canonical quantization and highlight the conceptual advantages of the algebraic approach to quantization.

Supersymmetric Backgrounds in $(1+1)$ Dimensions and Inhomogeneous Field Theory

We explore the quantization of a $$(1+1)$$ -dimensional inhomogeneous scalar field theory in which Poincaré symmetry is explicitly broken. We show the ‘classical equivalence’ between a scalar field theory on curved spacetime background and its corresponding inhomogeneous scalar field theory. This implies that a hidden connection may exist among some inhomogeneous field theories, which corresponds to general covariance in field theory on curved spacetime. Based on the classical equivalence, we propose how to quantize a specific field theory with broken Poincaré symmetry inspired by standard field theoretic approaches, canonical and algebraic methods, on curved spacetime. Consequently, we show that the Unruh effect can be realized in inhomogeneous field theory and propose that it may be tested by a condensed matter experiment. We suggest that an algebraic approach is appropriate for the quantization of a generic inhomogeneous field theory. 

/pdf/toward-quantization-of-inhomogeneous-field-theory-13lscvj8.pdf

Sang-A Park

Papers

AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model

Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy

Supersymmetric Backgrounds in $(1+1)$ Dimensions and Inhomogeneous Field Theory

Toward quantization of inhomogeneous field theory