To address whether one-loop corrections lift the classical pseudo-moduli space without explicitly computing the Coleman-Weinberg potential, we analyze the structure of the given supersymmetric theory and make field redefinitions to simplify the interaction.

Key Observations:

1. Superpotential Structure: The superpotential is ( W = \frac{1}{2} h_1 X \Phi_1^2 + \frac{1}{2} h_2 \Phi_2 \Phi_...

Write the superpotential so that the only combination of X and Φ2 that talks to Φ1 is manifest: W = 1/2 Φ1^2 (h1 X + h2 Φ2) + f X.

Make a linear, unitary change of variables in the X–Φ2 plane:

• S ≡ (h1 X + h2 Φ2)/h,
• T ≡ (−h2 X + h1 Φ2)/h, with h ≡ √(|h1|^2 + |h2|^2).

In this basis, W = 1/2 h S Φ1^2 + f (h1 S − h2 T)/h.

Two immediate consequences follow:

• SUSY breaking (tree level): Along t...

Yes – there is a quick, essentially algebraic, way to see that the 1-loop Coleman–Weinberg potential cannot depend on the classical moduli of the model.
All one needs is

• a linear field redefinition that isolates the only combination of fields that actually enters the interactions, and
• the fact that for a single massive chiral multiplet the 1-loop super-trace is independ...

Yes. Because the apparent “interaction’’ between the field that breaks SUSY and the other fields can be removed by a linear, unitary redefinition of the chiral multiplets, one can see immediately – without writing the Coleman-Weinberg formula – that no one–loop potential for the pseudomodulus is generated. In this basis the model is nothing but the Polonyi model plus an ordinary O’Raifeartai...

This is an interesting question about understanding the structure of a SUSY model without explicit calculation. Let me analyze this systematically.

Analysis of the Model

The superpotential is:

First, let's understand why SUSY is broken and identify the pseudo-moduli space.

SUSY Breaking

The F-term conditions are: -...

W = (1/2) h1 X Φ1² + (1/2) h2 Φ2 Φ1² + f X.

We are told that: (i) Supersymmetry is spontaneously broken. (ii) The one-loop corrections do not lift the classical pseudo-moduli space.

The question asks: can we argue (ii) without explicitly computing the Coleman-Weinberg potential? Spe...

This is an excellent question that gets at the heart of how to understand the structure of supersymmetric theories without getting bogged down in detailed calculations. The intuition to look for a field redefinition is exactly right. Here is a simple argument for why a subspace of the pseudo-moduli space remains flat at one-loop.

The Simple Argument

The argument rests on performing a specifi...

A very short way to see that nothing “mystical’’ is going on at one‐loop is simply to notice that all of your cubic couplings

W  = ½ h₁ X φ₁²  + ½ h₂ φ₂ φ₁²  + f X

depend only on the single linear combination

Σ ≡ h₁ X  +  h₂ φ₂

and that the orthogonal combination

T ≡ − h₂ X  + h₁ φ₂

never appears except in the term f X. In fact one easily checks that if you rewrite

...

Understanding Why One-Loop Corrections Don't Lift the Pseudo-Moduli Space

To answer this question, we need to show that one-loop corrections don't lift the classical pseudo-moduli space without explicitly calculating the Coleman-Weinberg potential. This can be done through an appropriate field redefinition that reveals the underlying structure of the theory.

Analysis of the Original Model

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