Questions tagged [supersymmetry]
A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.
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What is a Majorana spinor-vector gravitino?
I started to read about superstring theory, I do not have a good basis on SUGRA but I got asked to directly jump into superstrings.
Following ``Basic concepts of String Theory'' (Springer), I have two ...
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Ground state vertex operator in superstring theory
In Tongs' "String Theory" lectures chapters 5.4.1-5.4.2 Tong referred to alternative way to find the mass of the different string states using suitable operators, and then integrating the ...
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Counting States for $N$ SUSY in Wess and Bagger [closed]
In Wess and Bagger's book, we calculate how many states are there for massive cases under $N$ SUSY.
We couldn't follow the table on page 14. What is "Spin" here (absolute value?), and how ...
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Degrees of freedom in the early universe with MSSM?
As nicely summarized on P4 in On effective degrees of freedom in the early universe here; at high temperatures where all the particles of the Standard Model are present, we have 28 bosonic and 90 ...
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The difference between High energy SUSY and low energy SUSY
In the literature and comments, I have met two pieces of jargon:
Low energy SUSY,
High energy SUSY
I'm confused about the technical and well-defined conceptual differences between the two type of ...
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Project for Elementary Particle Physics Course
Good day! Are there any publicly available dataset in the field of particle physics that can be treated as time series? I am hoping to use methods in white noise analysis to somehow determine ...
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Predicted Mass of Hypothetical Graviphoton
In (some) supersymmetry theories, a spin-1 gravivector or graviphoton is predicted (but has not yet been observed) to exist. My question: is there a consensus among theorists as to the mass (if any) ...
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Terminology for the "recursion relations" or "ladder/generating algebra" when working with ladder operators
Example/Background: When working with a SUSY QM system, for example, the $2D$ QHO with reduced units: $$\hat{H}=-\nabla^2+\rho^2$$
For this system, we have the creation/annihilation (ladder) operators:...
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How to calculate the amplitude for emission of a gravitino in unbroken supersymmetry?
I am studying supersymmetry and supergravity, and I have encountered the following problem:
Suppose that supersymmetry is unbroken. Show how to calculate the amplitude for emission of a gravitino of ...
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Conformal manifold of a supersymmetric field theory
I'm trying to understand what exactly is the conformal manifold of a theory. If I understand it right, the conformal manifold is the space of couplings.
From that point of view, it is just a subset ...
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Difference between $\mathcal{N}=2$ and $\mathcal{N}=(1,1)$ SUSY
In supersymmetry algebra, $\mathcal{N}$ refers to $I=1,2,.. \mathcal{N} $ in $Q^{I}_{\alpha}$. My question is what does it mean to write $\mathcal{N}=(1,1)$ superalgebra?
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${\cal N}=2$ SUSY Multiplet
In https://www.physics.uci.edu/~tanedo/files/notes/SUSYXD.pdf, on page 47, I found that for ${\cal N}=2$ SUSY (massless representation), we start with a state $|\Omega\rangle$ with helicity $\...
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CPT Symmetry and the CPT Conjugate in Supersymmetry
Consider a supersymmetric theory in $D=4$ dimensions with $\mathcal{N}$ supercharges, $Q^I_\alpha, \bar{Q}^I_{\dot{\alpha}}.$ When one builds massless particle representations of the SUSY algebra, one ...
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Coupling of supergravity to matter
Whereas the "derivation" of the pure supergravity Lagrangian seems to be rather straightforward, once it comes to combine supergravity with matter, i.e. for instance with an ungauged chiral ...
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SUSY and the BMS group
I'm watching this intro to Supersymmetry lecture by Nathan Berkovits and, at roughly 33 minutes, he mentions he is going to extend the Poincaré group in an essentially unique manner, where "...
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Supersymmetry transformation superstring theory [closed]
in the study of worldsheet supersymmetry which im using Becker/Becker/Schwarz we introduce the idea of superspace by introducing a coordinate $\theta^{A}$ in addition to our $\sigma^{\alpha}=(\sigma,\...
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What is the difference between Yang-Mills theory and ${\cal N}=4$ supersymmetric Yang-Mills theory (SYM) [closed]
I am a beginner trying to learn Quantum Field theories.
I understand the basics of Quantum Electrodynamics and the emergence of Feynman diagrams from the perturbative expansion of the generating ...
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Why can't a superpotential depend on a the hermitian conjugate of a superfield?
I am working through Srednicki's "Quantum Field Theory" and am at the chapter on the Minimal Supersymmetric Standard Model (MSSM).
In answer to why two higgs superfields are needed in the ...
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Momentum maps and supersymmetry
While reading a paper by Gaiotto et al., I stumbled upon the concept of momentum maps where they are used in section 2.1 to characterise the vaccum structure of some theory.
I tried reading the ...
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Can this SUSY anomaly disappear in higher dimensions?
I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects.
Explicit breaking of supersymmetry ...
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Are there enough parameters in standard model to falsify SUSY?
I know that the search for Higgs would be quite pointless if there was no estimation of its mass.
Namely the perturbative violation of unitatity, gave us an upper bound on its mass.Unitarity ...
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How exactly is spinor with Grassmann variables as component defined?
I'm reading K. Muller's Introduction to Supersymmetry about spinor representation. He said that the components of a spinor are Grassmann variables.
I understood Grassmann variables as follows. For a ...
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Relation between RG flow and space of vacua
When studying supersymmetric QFT's, it is very common to compute the moduli space of the theory by solving all F-term equation (derivatives of the superpotential). More precisely, one should also ...
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Minimal supersymmetric Standard Model Supersymmetry Breaking
I'm working through Srednicki's QFT book.
I'm at Chapter 96 where he covers the Minimal Supersymmetric Standard Model.
I understand that supersymmetry is not an exact symmetry and I understand that ...
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SUSY Algebra Anti-commutation Relation
I am trying to understand one of the anti-commutation relations of SUSY algebra. The lecture notes "Supersymmetry and Extra Dimensions" (PDF) taken by Flip Tanedo, says on p.29, due to the ...
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BPS States and Conditions: Definition and Significance in the Context of ADS/CFT
I am currently studying a paper similar to the one linked and I'm struggling to comprehend the concept of BPS (Bogomol'nyi-Prasad-Sommerfield) states/operators. The cited papers mention these terms ...
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Necessary but not Sufficient Existence Condition for Killing Spinors
A Killing spinor is defined by the Killing equations:
$$D_{\mu}\epsilon=\partial_{\mu}\epsilon + \frac{1}{4}{\omega_{\mu}}^{ab}\gamma_{ab}=0$$
From this we can derive the Necessary but not Sufficient ...
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Can the dimension of a highest-weight irrep be a non-integer?
This is my first time using stack exchange, so I am sorry for any formatting errors.
I am working on implementing the Racah-Speiser algorithm for $\mathfrak{psu}(2,2|4)$ superconformal multiplets. I ...
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(Basic) confusion about value of scalar-fermion vertex $\phi\psi_i\psi_j$ for Majorana fermions
If I have a toy model with $N$ Majorana fermions $\lbrace\psi_i\rbrace_{i=1,\ldots,N}$ and a scalar field $\phi$ where the interaction among the fields is
$$
\mathcal L_\text{int}= \sum_{i,j=1}^N
a_{...
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Is simple harmonic potential only example which is invariant under gauge transform (in SUSY/QM context)?
I'm junior student in physics major, and i didn't study QFT or other graduate course yet, just undergraduated QM. Recently I take brief explanation class about SUSY, and in the class I heard that ...
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Differences between Einstein Gravity and classical Supergravity?
Given that the main difference of super-spacetime and spacetime is in the Grassmann dimensions, I want to know about the main differences in terms of results and features or modifications, between ...
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Supercurrent of supersymmetric world-sheet action
In my string theory class we added (Majorana) fermions to the world-sheet and noticed that the combined boson+fermion action
$$S[X,\psi]=\int\mathrm{d}\tau\mathrm{d}\sigma\,
\left(\frac{1}{\alpha'}\...
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Analogue of Bargmann's theorem for Super Lie groups
Bargmann's theorem gives the criteria under which a projective representation of a Lie group $G$ can be lifted to a representation of its universal cover. More generally, if this criterion, namely $H^...
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Trace identity for spin matrices in supersymmetry
My question comes from Srednicki chapter 95, specifically equation 95.75.
Srednicki gives an identity to evaluate the trace of his left-handed fermion matrices:
$$Tr(S^{\mu\nu}_LS^{\rho\sigma}_L)$$
He ...
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$SU(2)$ with non-standard matter Supersymmetry
Consider the theory with 1 chiral multiplet $Φ$ of isospin 1 and 2 chiral multiplets $𝑄^I$ of isospin 1/2. The superpotential is $𝑊 = 0$.
I found the dimension of the moduli space as 4 by the Higgs ...
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Grassmann parameter in supersymmetry
Let's consider a free Wess-Zumino Lagrangian given by
$$\mathcal{L} = \partial^{\mu}\overline{\phi}\partial_{\mu}\phi + i\psi^{\dagger}\overline{\sigma}^{\mu}\partial_{\mu}\psi\tag{1}$$
Whose ...
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Superfields over superspaces
Suppose that we have an $n$-dimensional vector space $X$ together with a basis $\{\theta_i\}^n_{i = 1}\in X$.
$$\bigwedge(X) = \mathbb{C}\oplus\bigwedge^1(X)\oplus\bigwedge^2(X)\oplus\cdots\oplus\...
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Bosonic representation of delta function for Grassmann-even quantity
Suppose I have 2 Grassmann scalars $\theta$ and $\bar{\theta}$ and form the bosonic quantity $X = \bar{\theta}\theta$. Is there a purely bosonic representation of the delta function $\delta(X - \...
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Dynkin labels of $psu(2,2|4)$
I'm currently studying the superconformal algebra $psu(2,2|4)$, but I'm having trouble understanding its representation.
Following arxiv:1012.4004
I know that the maximal compact subalgebra is su(2) $\...
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Spin of covariant derivatives in 3D $\mathcal{N}=2$ superspace
Consider the 3D $\mathcal{N}=2$ superspace covariant derivatives $D_\alpha$ and $\bar D_\beta$, which have the following anti-commutation relations
$$\{ D_\alpha, \bar D_\beta \}=-2i \gamma^\mu_{\...
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Gauge transformation of vector superfields
I am working my way through Srednicki and am at Chapter 95 which introduces supersymmetry.
$\newcommand\dag\dagger$
In Chapter 95, Srednicki introduces the idea of a vector superfield, which he says ...
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Why must Lie superalgebras always contain both $Q$ and $\bar{Q}$?
In four dimensions Lie superalgebras naturally arise by relaxing the presupposition in the Coleman-Mandula theorem that the symmetry is not classified by a Lie algebra. It is then typically stated ...
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The "survival hypothesis" and supersymmetry
Tidying up my old papers I came across my supersymmetry notes from the late 80s. I thought I'd reread them. They may be out of date now. I find the mathematics somewhat comprehensible but not the ...
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Dyon Equivalence and Democracy Tranformations in Seiberg-Witten Theory
I am currently studying Seiberg Witten theory's strong and weak coupling spectrum from the paper of Ferrari-Bilal The Strong Coupling Spectrum of Seiberg Witten Theory.
I have a couple of doubts ...
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Deriving world-sheet super currents
I am trying to derive the world-sheet super currents (Polchiski eq 10.1.8), could someone describe or give some hints on how these are derived?
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Derivatives as "dynamical variables of the theory"?
This question will probably sounds very broad.
So, I work with classical general relativity, a bit of field theory and semiclassical gravity. I have a friend, though, that works with things like ...
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Holomorphic sections that lead to the original parameterization of the gauged STU model
The original action, given in 9903214, comes from the $\mathcal{N} = 2$ abelian truncation of the maximal $\mathcal{N} = 8$, $SO(8)$ gauged supergravity that can be obtained from $S^
7$
reduction of ...
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What is BPS state?
I am preparing a presentation about black holes thermodynamics in string theory. Both in polchinski and in many famous articles there is a discussion about BPS and I am not able to understand why it ...
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Does every field theory have a susy completion?
I have a limited understanding of supersymmetry. I understand that a theory that has supersymmetry can have the supersymmetry broken, leaving at low energy what looks like an ordinary quantum field ...
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Generalized Stokes theorem in superspace
Do the generalized Stokes theorem apply in superspace? Any issues or uncommon behaviour of the gradient, divergence and rotational in superspace?
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