arXiv subjects

Christian Ferko

Publications and source records attributed to Christian Ferko.

45 records · Page 3Linked to original sources

arXiv2022

$T \overline{T}$ Deformations of Supersymmetric Quantum Mechanics

We define a manifestly supersymmetric version of the $T \overline{T}$ deformation appropriate for a class of $(0+1)$-dimensional theories with $\mathcal{N} = 1$ or $\mathcal{N} = 2$ supersymmetry, including one presentation of the super-Schwarzian theory which is dual to JT supergravity. These deformations are written in terms of Noether currents associated with translations in superspace, so we refer to them collectively as $f(\mathcal{Q})$ deformations. We provide evidence that the $f(\mathcal{Q})$ deformations of $\mathcal{N} = 1$ and $\mathcal{N} = 2$ theories are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of $2d$ theories with $\mathcal{N} = (0,1)$ and $\mathcal{N} = (1,1)$ supersymmetry, respectively. In the $\mathcal{N} = 1$ case, we present two forms of the $f(\mathcal{Q})$ deformation which drive the same flow, and clarify their equivalence by studying the analogous equivalent deformations in the non-supersymmetric setting.

hep-th↗

arXiv2022

On Current-Squared Flows and ModMax Theories

We show that the recently introduced ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equation driven by a quadratic combination of stress-energy tensors. The operator associated to this flow is a $4d$ analogue of the $T\bar{T}$ deformation in two dimensions. This result generalizes the observation that the ordinary Born-Infeld Lagrangian is related to the free Maxwell theory by a current-squared flow. As in that case, we show that no analogous relationship holds in any other dimension besides $d=4$. We also demonstrate that the $\mathcal{N}=1$ supersymmetric version of the ModMax-Born-Infeld theory obeys a related supercurrent-squared flow which is formulated directly in $\mathcal{N}=1$ superspace.

hep-th↗

arXiv2022

Supersymmetry and Irrelevant Deformations

The $T \overline{T}$ operator provides a universal irrelevant deformation of two-dimensional quantum field theories with remarkable properties, including connections to both string theory and holography beyond $\mathrm{AdS}$ spacetimes. In particular, it appears that a $T \overline{T}$-deformed theory is a kind of new structure, which is neither a local quantum field theory nor a full-fledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of Poincaré symmetry which relates bosonic and fermionic degrees of freedom. It is natural to ask what one can learn about irrelevant deformations in supersymmetric quantum field theories. In this thesis, we describe a presentation of the $T \overline{T}$ deformation in manifestly supersymmetric settings. We define a "supercurrent-squared" operator, which is closely related to $T \overline{T}$, in any two-dimensional theory with $(0, 1)$, $(1, 1)$, or $(2, 2)$ supersymmetry. This deformation generates a flow equation for the superspace Lagrangian of the theory, which therefore makes the supersymmetry manifest. In certain examples, the deformed theories produced by supercurrent-squared are related to superstring and brane actions, and some of these theories possess extra non-linearly realized supersymmetries. We then show that $T \overline{T}$ defines a new theory of both abelian and non-abelian gauge fields coupled to charged matter, which includes models compatible with maximal supersymmetry. Most of this thesis is adapted from previous publications. However, the final chapter presents new results on $T \overline{T}$-like deformations of general gauge theories in an arbitrary number of spacetime dimensions; this analysis has not appeared in past work.

hep-th↗

arXiv2022

Gravitational Memory and Compact Extra Dimensions

We develop a general formalism for treating radiative degrees of freedom near $\mathscr{I}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the BMS group to include angle-dependent isometries of the internal space. We apply this formalism to study memory effects, which are expected to be observed in future experiments, that arise from bursts of higher-dimensional gravitational radiation. We outline how measurements made by gravitational wave observatories might probe properties of the compact extra dimensions.

gr-qc↗

arXiv2020

Defining the $T \overline{T}$ Deformation on $\mathrm{AdS}_2$

We show that the $T \overline{T}$ deformation of two-dimensional quantum field theory on $\mathrm{AdS}_2$ is well-defined and solvable at the quantum level. Flow equations for the energy spectrum and partition function are derived in analogy with the flat space case. As a non-trivial check, we perturbatively compute the deformed energy spectrum for the case of a free scalar field. We analyze the high energy density of states of the deformed theory and find a Hagedorn growth of states.

hep-th↗

arXiv2020

A Non-Abelian Analogue of DBI from $T \overline{T}$

The Dirac action describes the physics of the Nambu-Goldstone scalars found on branes. The Born-Infeld action defines a non-linear theory of electrodynamics. The combined Dirac-Born-Infeld (DBI) action describes the leading interactions supported on a single D-brane in string theory. We define a non-abelian analogue of DBI using the $T \overline{T}$ deformation in two dimensions. The resulting quantum theory is compatible with maximal supersymmetry and such theories are quite rare.

hep-th↗

arXiv2019

$T\bar{T}$ Flows and (2,2) Supersymmetry

We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $T\bar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in the physical potential which modify the vacuum structure. This suggests that irrelevant deformations of $T\overline{T}$ type might also affect infrared physics.

hep-th↗

arXiv2019

Non-Linear Supersymmetry and $T\bar T$-like Flows

The $T\bar{T}$ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain $\mathcal N =(2,2)$ models in two dimensions, where we observe an intriguing similarity with known $\mathcal N=1 $ models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from $T\bar{T}$-like flow equations. We show that in four dimensions this is indeed the case for $\mathcal N=1 $ Born-Infeld theory, as well as for the Goldstino action for spontaneously broken $\mathcal N=1 $ supersymmetry.

hep-th↗

arXiv2019

Supersymmetry and $T \overline{T}$ Deformations

We propose a manifestly supersymmetric generalization of the solvable $T \overline{T}$ deformation of two-dimensional field theories. For theories with $(1,1)$ and $(0,1)$ supersymmetry, the deformation is defined by adding a term to the superspace Lagrangian built from a superfield containing the supercurrent. We prove that the energy levels of the resulting deformed theory are determined exactly in terms of those of the undeformed theory. This supersymmetric deformation extends to higher dimensions, where we conjecture that it might provide a higher-dimensional analogue of $T \overline{T}$, producing supersymmetric Dirac or Dirac-Born-Infeld actions in special cases.

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