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Questions tagged [supersymmetry]

A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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Gauss law, gauge and global symmetries

I am reading Witten's paper on the confinement/deconfinement phase transition in $\mathcal{N}=4$ $\mathrm{SU}(N)$ SYM theory. I am a bit stuck at section "Confinement" at Finite Volume, page ...
Davide Morgante's user avatar
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Statement clarification: When do we have $\Delta = \frac{d-1}{2} q_R$?

This statement is for SCFT, where $\Delta$ is the conformal weight, $q_R$ is the R-charge. How many supersymmetries do we need? Do we need chiral primary scalar, or just chiral scalar? How to derive ...
Kangning Liu's user avatar
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Super Hilbert space of SYM

I hope this message finds you well. I am currently try to understand explicitly, at least in some sense, $d=4$, ${\cal N}=4$ super Yang-Mills theory. What is the explicit construction of the super ...
d'Alembert's user avatar
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Superspace calculation: Converting the Kahler potential to superpotential?

In the Lecture notes of Tachikawa on 4d ${\cal N}=1$, in equation (3.2.12), which reads \begin{equation} \int d^4 \theta \delta K = - \frac{1}{2} \int d^2 \theta \overline{D}^2 \delta K + c.c.\tag{...
Kangning Liu's user avatar
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Confinement, Holographic QCD, Seiberg-Witten Theory

I have seen a bunch of articles that all try to show confinement using AdS/QCD or Holographic QCD method. I pretty much know that the lastest attempt to prove confinement based on breaking SUSY even ...
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Konishi operator anomalous dimension [closed]

The Konishi operators are operators in the ${\cal N}=4$ SYM theory and are given by: $$ K = \sum _{i=1}^6Tr\ (\phi^i\phi^i) $$ The 2 point function of this operator is: $$ \big\langle K(x)K(y)\big\...
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Article on 1D deformed quantum harmonic oscillator

Few years ago I was reading an article which I'm trying to find for quite some time but with no success so far. It was a paper about deformation of 1D quantum harmonic oscillator with continuous ...
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Proving conservation of supercurrent

I am trying to prove that the supercurrent $J^\mu = \gamma^{\nu \rho} F^A_{\nu \rho} \gamma^\mu \lambda^A $ is conserved in ${\cal N}=1$ SUSY Yang-Mills theory ( basically trying to reproduce equation ...
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Commuting/anticommuting properties of fermionic ghost fields in BRST Quantization

I was reading the paper "Batalin-Vilkovisky analysis of supersymmetric systems" (by Laurent Baulieu and others). I am struggling to understand how commutation/anticommutation relations of ...
Aravind Madhavan's user avatar
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Poincaré algebra and supersymmetric spaces

If i understand correctly, a supersymmetry algebra should contain as a subalgebra the Poincaré algebra, however for a supersymmetry algebra the corresponding supersymmetric (Minkowski) space has ...
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What are the implications of supersymmetry generators satisfying a majorana condition?

hoping to resolve some confusion I have about this paper (https://arxiv.org/abs/hep-th/9904017) regarding the holographic dual of a flow from ${\cal N}=4$ SYM to an ${\cal N}=1$ SUSY theory. Broadly ...
Cyrus R.O.'s user avatar
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Modified Special Geometry of SUSY Moduli Space

It is known that the Coulomb branches of 5d $\mathcal{N}=1$ and 4d $\mathcal{N}=2$ SUSY (both have eight supercharges) satisfy special geometry. This means that there exists a holomorphic prepotential ...
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Noether's theorem for supersymmetry [duplicate]

I know that Noether's theorem states that all symmetries of the universe correspond to some conservation law. If supersymmetry were true, would there be a new conservation law? In other words, does ...
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How does spontaneous supersymmetry breaking lead to different masses between superpartners?

For the past few days I've been studying supersymmetric quantum mechanics. My main sources that I use are David Tong's lecture notes on supersymmetric quantum mechanics, as well as Edward Witten's ...
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"Fourier Transformation" of angle spinors to twistor variables

This relates to the derivation of equation (5.15) if Elvang and Huang's textbook. The idea is to transform the spinor helicity variables we are using, $(|i\rangle_{\dot{a}},[j|^a)$ to go into twistor ...
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N=4 Supersymmetric Ward identity

(This question pertains to exercise 4.13 of Elvang and Huang's textbook (which used to be lecture notes). This is not for a class, just to learn some new tools for work). Consider the expansion of the ...
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Prepotential in 5d $\mathcal{N}=1$ with higher-derivative correction

The (bosonic part of the) action of five-dimensional $\mathcal{N}=1$ supergravity coupled to a number of vector multiplets reads $$S=\frac{1}{2\kappa_5^2}\int\star(R-\frac{1}{2}h_{ij}(\phi)\partial-\...
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Picture Number in String Vertex Operator

How can I know what is the Picture of a particular vertex operator? For example in 8.3.15 in Polchinski's book Vol.1, the Vertex Operators for the Enhanced Gauge symmetry are given by \begin{equation}...
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Asymptotic form of wavefunctions in case of $k$ one-dimensional asymptotic regions

I'm reading the paper Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics, and am struggling to understand some things about section 2. In particular eqn 2.2, and how to think about the ...
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Effects of a hypothetical "proton-decay bomb" for a fictional story [closed]

I'm writing a science fiction story in which I need a devastating weapon of mass destruction that is far worse than nuclear bombs. For some reason, I'm fascinated by the idea of a "proton-decay ...
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Supersymmetric Wess Zumino term and Fierz identities in $d=10$

When studying the Green-Schwarz formalism of superstring, we came across the following term (the Wess Zumino term) in the action \begin{align*} S_{WZ} = \frac{1}{2 \pi \alpha} \int d^2 \sigma [ \...
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Confusion about whether a fermion field and its conjugate as an Grassmann number

I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions. In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\...
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Silly confusion about gauge invariance in supersymmetric Lagrangians - in particular, in the ${\cal N}=1$ superfield formulation of ${\cal N}=4$ SYM

Hoping to resolve a simple confusion I have about supersymmetric gauge theory, one which I ran into while trying to understand the ${\cal N}=1$ superfield formulation of ${\cal N}=4$ supersymmetric ...
Cyrus R.O.'s user avatar
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On the $0$ representation of massive multiplets

So my doubt involves the massive multiplet of $\mathcal{N}=2$. I am not being able to deduce what particles does the states represents. For example, The $\mathcal{N}=2$ massive short hypermultiplet $s=...
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Introductory Reference for Supergravity

I have finished quantum field theory and general relativity and want to read about supergravity. I have read about supersymmetry from the demystify series and the supersymmetry part of Wess and Bagger'...
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Lagrangian of chiral superfield

Consider a number of chiral superfield $\Phi_i$ with components $A_i$, $\psi_i$, $F_i$, respectively a complex scalar, a 2-component Weyl fermion and an auxiliary complex scalar. The most general ...
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For a chiral superfield, $\overline{D}^2 D^2 \Phi = 16 \partial^2 \Phi$

When looking for the derivation of the Kahler potential, generally is assumed the following idendity: For a Chiral superfield $\Phi$, we have $$\overline{D}^2 D^2 \Phi = 16 \partial^2 \Phi$$ But ...
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If $H$ anniliates a state, must $Q$ and $Q^\dagger$ also annihilate the state?

Suppose we have a a Hamiltonian, $H$. And suppose also we have some operator $Q$ such that $\{Q, Q^{\dagger}\} = H$, and $Q^2 = 0$. If we find a state $|\psi \rangle$ such that $Q|\psi \rangle = Q^{\...
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What is the Lagrangian for the interaction of graviphoton with matter?

There are some models that postulate the existence of graviphoton. What is the Lagrangian for the interaction of graviphoton with matter?
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How the supercharge operators act on superfields in quantum mechanics, and the adjoints of supercharges?

I'm watching this lecture on introductory Supersymmetry (Clay Cordova, 2019 TASI lecture 2 on Supersymmetry). My question relates to the first 20minutes or so. The lecturer is introducing Superfields ...
Gleeson's user avatar
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Real representation of smallest dimension of Clifford Algebra with $d$ generators

I'm trying to understand the model described in this paper. I have a question about a claim they make. From page 2: To describe the fermionic degrees of freedom let, as a preliminary \begin{align*} ...
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Axial Chiral Anomaly

I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
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Nekrasov partition function

In the celebrated paper Seiberg-Witten prepotential from instanton counting by N. Nekrasov I can't quite understand some parts of section (2.3). The Nekrasov partition function is defined via \begin{...
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Is there an exact correspondence between Seiberg-Witten theory and mirror symmetry?

Seiberg-Witten solution gives an algebraic geometrical description of the quantum moduli of 4d $\mathcal{N}=2 $ SUSY gauge theory. However, the solution seems purely constructive and does not enjoy ...
Yankun Ma's user avatar
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Can we define topological order in the context of QFT?

Topological order is defined to be a phase that has ground state degeneracy (GSD) not described by the Landau SSB paradigm but exhibits some Long Range Entanglement property. Mathematically, it is ...
Yankun Ma's user avatar
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Seiberg-Witten Theory and the Kähler manifold

Starting from the Kähler potential $$\mathcal{L}=\frac{1}{4\pi} Im(\int d^{4}\theta tr(\Phi^{\dagger}e^{2V}\Phi),$$ How do we integrate out to get the following Lagrangian: $$\mathcal{L}=\frac{1}{4\pi}...
Archie C's user avatar
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References for Hanany-Witten setups

What are some good, possibly modern, references for Hanany-Witten brane setups? I know the one of Giveon and Kutasov: Brane Dynamics and Gauge Theories, but I would like to have some more since this ...
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Thermodynamics of supersymmetric black hole

For a 4-dimenstional supersymmetric Kerr Newman black hole, we have $$\beta\Omega=2\pi i$$, and the index $$\text{Tr}[(-)^Fe^{-\beta(M-Q)}]=e^{S+\beta\Omega J}$$ with $S+\beta\Omega J$ being $\beta$ ...
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Problem evaluating an anticommutator in supersymmetric quantum mechanical gauge theory

I am trying to reproduce the results of a certain paper here. In particular, I'm trying to verify their eqn 5.31. The setup is N = 4 gauge quantum mechanics, obtained by the dimensional reduction of N ...
Gleeson's user avatar
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Representation theoretic constraints in SUSY algebra

Let's try to build from scratch the SUSY commutator $[Q_\alpha^I, P_\mu]$. We know that the result of this commutator must be a fermonic generator belonging to $(1/2, 0)\otimes(1/2,1/2) \simeq (1, 1/2)...
Jack Euler's user avatar
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1 answer
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Understanding a supersymmetric quantum mechanical gauge theory model

I'm studying this paper on supersymmetric ground state wavefunctions. In section 5 "quantum mechanical gauge theories", it says: "We begin with the ${\cal N} = 2$ gauge theory which ...
Gleeson's user avatar
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Local Supersymmetry and Space-time Metric

So following from Simple Supergravity (arxiv:2212.10044), on page 5, it's written that Only the spacetime metric can couple to the energy-momentum tensor... Can anyone explain why it must be the ...
Alex's user avatar
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Fermionic and bosonic degrees of freedom of a vector superfield

I am currently studying supersymmetry with the SUSY primer of Stephen P. Martin (https://arxiv.org/abs/hep-ph/9709356) and there seem to be not equally many bosonic and fermionic degrees of freedom (...
FlavonBSM's user avatar
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1 answer
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What does $\mathcal{N}=2$ mean? [closed]

I have seen in some places (especially in the context of theoretical physics) the notation $\mathcal{N}=2$, but I'm not that capable of reading and understanding these materials, thus I'm now ...
BoyanLiu's user avatar
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Looking for a source to explain the Process of Topological twisting

as the title suggests I am looking for papers or other material that explains the notion of Topological twisting as it appears in the context of certain SUSY algebras. Concretely I am interested in ...
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1 answer
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Deducing charges from a Lagrangian, in supersymmetric quantum mechanics

I'm trying to read through this paper called "Supersymmetric Ground State Wavefunctions". Half way down page 4, is says "We begin by reviewing Witten's original model which is defined ...
Gleeson's user avatar
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Berezin Integration, confirming an measure is invariant

I am working through the Mirror Symmetry book, available here. I already had a question about an earlier part of the same Exercise 9.2.1 on page 157: We are given the following action with one boson ...
Gleeson's user avatar
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2 votes
1 answer
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Confirming an action is invariant under a supersymmetric transformation

I am studying chapter 9 of the book Mirror Symmetry, available here. My question is relating to page 156/157 where Supersymmetry is being introduced for the first time in QFT in 0-dimensions. We are ...
Gleeson's user avatar
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Decomposition of vector bundle in $M$-theory

I was studying this paper where the authors construct some field theory solutions by wrapping M5-branes on holomorphic curves on Calabi-Yau. I have some questions about their construction. What they ...
Davide Morgante's user avatar
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Is it possible to construct theory where fermions are force carriers?

Supersymmetry is a model based on symmetry between bosons and fermions. Bosons carry force and they are described by potentials. Fermions are matter particle and they are described by wavefunctions. ...
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