[Paper Review] Corpuscular Breaking of Supersymmetry

Gia Dvali, César Gómez|arXiv (Cornell University)|Jun 23, 2014

Black Holes and Theoretical Physics7 references3 citations

TL;DR

This paper proposes that topological solitons, including domain walls and D-branes, are quantum coherent states of underlying corpuscles—fundamental quanta whose collective behavior gives rise to non-perturbative structures. Using a functional integral formalism over corpuscle number distributions, it shows that quantum corrections from these constituents break supersymmetry generically, with the breaking scale set by the string coupling and D-brane tension, offering a built-in, stable mechanism for SUSY breaking in string theory.

ABSTRACT

Are topological solitons elementary or composites? We answer this question by drawing up a corpuscular formalism in which solitons are coherent states of quantum constituents. This naturally leads to a functional integral representation, in which the classical saddle point is reached as the most probable distribution of corpuscles in the $\hbar = 0$ limit and where quantum corpuscular corrections correspond to excursions away from such a distribution that occur only for finite $\hbar$. Several striking features come up. Topological charge emerges as a collective flow of quantum numbers carried by individual corpuscles. Moreover, the corpuscular corrections are not reducible to any known form of quantum corrections, such as loop expansions in the coupling constant $\hbar g^2$ or semiclassical $e^{-1/\hbar g^2}$ effects. Corpuscular corrections are stronger and appear already at order $\sqrt{\hbar g^2}$. In SUSY theories quantum corpuscular corrections generically break supersymmetry. We show that a domain wall which perturbatively is a BPS state, violates all supersymmetries when the corpuscular effects are taken into account. The extension of the corpuscular structure to $D$-branes can lead to a built-in supersymmetry breaking mechanism in string theory, insensitive to technicalities such as moduli stabilization, with the SUSY breaking scale set by the string coupling times the $D$-brane tension.

Motivation & Objective

• To resolve the foundational question of whether topological solitons are fundamental or composite by modeling them as coherent states of quantum corpuscles.
• To develop a functional integral framework for solitons based on the most probable distribution of corpuscles in the ħ → 0 limit.
• To identify a new class of quantum corrections—corpuscular corrections—that are non-analytic in ħg² and distinct from standard loop or instanton effects.
• To investigate how these corpuscular effects lead to spontaneous supersymmetry breaking in BPS states like domain walls and D-branes.
• To propose a stable, intrinsic mechanism for supersymmetry breaking in string theory, insensitive to moduli stabilization, with the breaking scale set by the string coupling.

Proposed method

• Model solitons as coherent quantum states |sol⟩ in the Fock space of corpuscles, defined by momentum-dependent average occupation numbers Nₖ.
• Express the soliton state as a functional integral over number distributions nₖ, weighted by an effective action S_eff(nₖ) = −½∫dk (Nₖ − nₖ ln Nₖ + ln(nₖ!)).
• Identify the classical saddle point as the most probable distribution nₖ^(sd) ≈ Nₖ − ½ + O(1/Nₖ), distinct from the naive classical limit nₖ^(class) = Nₖ.
• Derive corpuscular corrections as quantum fluctuations around nₖ^(sd), which are non-perturbative and non-analytic in ħg², appearing already at order √(ħg²).
• Apply the formalism to Wess-Zumino domain walls and D-branes, identifying the tachyon condensate as the corpuscular medium and relating Nₖ to brane charge and tension.
• Establish a dictionary between the Wess-Zumino model and D-branes via T = 0 potential height matching, leading to N ≈ ̂N² and L ≈ Lₛ, with corrections scaling as gₛ.

Experimental results

Research questions

• RQ1 Can topological solitons be understood as composite states of quantum corpuscles rather than fundamental entities?
• RQ2 What is the functional integral representation of a soliton in terms of corpuscle number distributions, and how does it generalize the classical saddle point?
• RQ3 How do corpuscular corrections differ from standard quantum corrections such as loop expansions or e^−1/ħg² effects?
• RQ4 To what extent do corpuscular effects break supersymmetry in classically BPS solitons like domain walls?
• RQ5 Can the corpuscular structure of D-branes in string theory provide a stable, intrinsic mechanism for supersymmetry breaking at the string scale?

Key findings

• Corpuscular corrections arise from quantum fluctuations around the most probable distribution of corpuscles and are non-analytic in ħg², appearing at order √(ħg²), unlike standard loop corrections.
• Topological charge emerges as a collective flow of quantum numbers carried by individual corpuscles, not as a property of a single field configuration.
• In supersymmetric theories, corpuscular corrections generically break all supersymmetries: a classically BPS domain wall becomes non-BPS when quantum corpuscular effects are included.
• For D-branes, the corpuscular treatment leads to a supersymmetry-breaking effect of order gₛ, with the breaking scale set at the string scale, independent of moduli stabilization.
• The corpuscular mechanism of SUSY breaking is stable and intrinsic—non-BPS branes do not decay because the corrections only affect the BPS condition, not the topological or RR charge.
• The effective scale of supersymmetry breaking in the worldvolume theory is suppressed by gₛ relative to the D-brane tension, which scales as 1/gₛ, yielding a string-scale breaking scale.