Having Fun with Theoretical Physics

As solitonic solutions, Dp-branes acquire effective nonlinear descriptions whose bosonic parts are given by the Dirac-Born-Infeld action. The existence of these effective nonlinear descriptions is no accident and follows directly from the partial supersymmetry breaking N = 2 → N = 1. In general, the memory of a spontaneously broken symmetry does not fade completely and is captured through nonlinear realizations of that symmetry. In this fashion, the effective description of Dp-branes must be consistent with the linear representations of the surviving supersymmetry and also with the nonlinear realizations of the second broken supersymmetry. Such nonlinear realizations of supersymmetry are defined via nonlinear constraints which generate precisely the Born-Infeld type actions of D-branes.

In the work with Konstantinos Koutrolikos [2206.01607], we focus on the effective descriptions of D2-branes, which play important roles in the Type IIA string theory. Using the Goldstone multiplet interpretation of the action and the method of nilpotent superfields, we construct a 3D superspace description which makes the first supersymmetry manifest and realizes the second, spontaneously broken, supersymmetry nonlinearly. We find that appropriate Goldstone multiplets and their effective superspace actions are generated by the N = 2, D = 3 vector and tensor multiplets after expanding them around a nontrivial vacuum and enforcing constraints that eliminate additional degrees of freedom. We show both descriptions are related by a duality transformation which results in the inversion of a dimensionless parameter. The explicit bosonic and fermionic parts of the effective spacetime action are derived. Finally, we consider the deformation of the superspace action by the characteristic Chern-Simons-like mass term of vector multiplet in 3D.

# Nonlinear SUSY and Dp-brane Effective Actions

## TTbar-like Flows

A lot of recent efforts have suggested that nonlinearly realized (super)symmetries might also arise from TTbar-like flow equations. My recent work with Ferko, Huang, Koutrolikos, and Tartaglino-Mazzucchelli [2302.10410] provides further evidence for this connection. Specifically,

We show that the 3d Born-Infeld theory can be generated via an irrelevant deformation of the free Maxwell theory. The deforming operator is constructed from the energy-momentum tensor and includes a novel non-analytic contribution that resembles root-TTbar which is the key to evading a previous no-go result saying that the TTbar flow equation can only lead to Born-Infeld type solutions in 4D.

We find that a similar operator deforms a free scalar into the scalar sector of the Dirac-Born-Infeld action, which describes transverse fluctuations of a D-brane, in any dimension.

We analyze trace flow equations and obtain flows for subtracted models driven by a relevant operator.

In 3d, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in N=1 superspace, where the deforming operator is built from supercurrents. We demonstrate that two supersymmetric presentations of the D2-brane effective action, the Maxwell-Goldstone multiplet and the tensor-Goldstone multiplet, satisfy superspace flow equations driven by this supercurrent combination.

To do this, we derive expressions for the supercurrents in general classes of vector and tensor/scalar models by directly solving the superspace conservation equations and also by coupling to N=1 supergravity.