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

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What is the difference between worldsheet supersymmetry and spacetime supersymmetry?

What is the difference between worldsheet supersymmetry and spacetime supersymmetry? For worldline formulation of fermions quantum mechanics, there is a supersymmetry. But the corresponding spacetime ...
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Detecting supersymmetry

What would scientists in particle colliders look for as evidence of supersymmetry?
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35 views

How can one determine whether two given Hamiltonians are supersymmetric partners?

Given two Hamiltonians in a general form of second order differential equations, how do I find out if they are SUSY partners or not? Given the factorisation of a Hamiltonian in the form of $a^\dagger ...
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105 views

A question from A. Zee's book

On page 463, it writes in eq. (3) $$4H=\Sigma_\alpha(Q_\alpha Q^\dagger_\alpha+Q^\dagger_\alpha Q_\alpha).\tag 3$$ And then it writes that this is followed by eq.(4) as $$\langle S| H|S\rangle=\frac{...
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Should the complex conjugate of a derivative of a Grassmann number include a sign?

Take a real Grassmann variable, by which I mean $\theta=\theta^*$. We have $$\int d\theta~ \theta =1,\qquad \frac{\partial}{\partial\theta}\theta=1$$ If I define the conjugation of Grassmann ...
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26 views

Second derivative of Kahler potential [closed]

Does the following second covariant (in terms of Kahler geometry) derivative of Kahler potential vanish? \begin{equation} K_{ij}\equiv\nabla_i\nabla_j K=0, \end{equation} \begin{equation} K_{i^*j^*}\...
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77 views

Derivation in Modern Supersymmetry by Terning

I am trying to do some calculations from Modern Supersymmetry by Terning and I am stuck on how he derived a particular term. Specifically, I am looking at 2.67 on page 27. My current work is below. $$...
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28 views

Anti-commutator relation of supercharges

Reading mutiple references on SUSY (e.g. Baer and Tata's Weak Scale SUSY and A SUSY Primer by S.P. Martin, arXiv:hep-ph/9709356), there seems to be different anti-commutation relation conventions for ...
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The super Grassmannian $G_{2|2}(4|4)$

In the paper, the super Grassmannian $G_{2|2}(4|4)$ is defined by (12)--(18). An element of $G_{2|2}(4|4)$ can be written as a $(2 | 2) \times (4 | 4)$ matrix of full rank modulo the left action by ...
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Notation of supermatrices

I am trying to understand supermatrices. First I want to know the notation of supermatrices. In the paper, it is mentioned $(2|4|2) \times (2|2)$ supermatrices. What are $(2|4|2) \times (2|2)$ ...
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Vacuum energy and supersymmetry [closed]

Let us assume that dark energy is the energy of the vacuum. The density of this vacuum energy has been measured to be about $10^{-26}$ $kg/m^3$. Using the Compton wavelength formula, $\lambda=h/mc$, ...
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How to find curved superspace vielbein and connection?

Need help with finding total curved superspace vielbein and connection in terms of SUGRA multiplet components (graviton, gravitino, auxiliary real vector and complex scalar). In Wess and Bagger ...
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74 views

“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
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16 views

How relevant are non-minimal Kahler potentials in supergravities?

Does it make sense to consider non-minimal Kahler potential of the form $K\sim|\phi|^4$? Or, to slightly rephrase the question, can we altogether ignore scalar kinetic terms with coefficients ...
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76 views

Why is Seiberg duality called an electromagnetic duality?

An electromagnetic duality is a duality that maps electric to magnetic degrees of freedom of two distinct theories. Apart from source-less Maxwell electrodynamics, other theories require magnetic ...
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39 views

What is a “Scalar Manifold”?

I'm trying to understand a recent paper working within the context of $\mathcal{N}=8$ gauged supergravity with gauge group $\rm{SO}(6)$. There are a number of statements along the lines of: "...the ...
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39 views

Supersymmetry algebra convention?

As derived for instance in this review (page 23-24), the supersymmetry algebra involving grassmann valued generators $Q_\alpha$ and ${\bar Q}_{\dot\alpha}$ is given by: $$[Q_\alpha,M^{\mu\nu}]=(\...
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Confusion about supergravity multiplet

I have a bit of confusion with the following consideration. Generally, to impose some BPS condition (i.e. to check if some multiplet preserves some SUSY charges) one imposes to zero the SUSY ...
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80 views

Supersymmetry and grand unification

I came across this diagram in my introductory particle physics class. Given the fact that SUSY can make the plot look suspiciously nice, what can we do with it? Also, electromagnetism has been ...
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Supersymmetrizing bosonic actions at higher orders

Given only the bosonic terms of a supersymmetric action, using a knowledge of the (local) supersymmetry transformations, is there a systematic way of reconstructing the fermionic terms? More generally,...
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Equivariance Relation - Superconformal Hypermultiplets

I'm concerned with equation 2.24 of http://arxiv.org/abs/1601.00482 The superconformal hypermultiplets in this paper have a conic hyperkahler target manifold and the authors want to gauge some ...
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35 views

Which supersymmetry principles make the axio-dilaton field in F-theory holomorphic?

I am following the lecture notes on F-theory by T. Weigand . On page 7 he states that when considering F-theory as the strong coupling limit of type IIB orientifolds with D-branes, the axio-dilaton ...
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Supersymmetric background and fermion variations

I'm trying to understand some basic questions about supersymmetric theories in curved backgrounds and supergravity. If I understand it correctly, there's a condition for a background to preserve SUSY, ...
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Why supersymmetry requires either left or right movers to vanish for a $S^1$ compactification

In the chapter on Black holes in string theory (Section 11.4, page 584 near equation 11.94) in the book by Becker, Becker and Schwarz, they write [...] let us consider a single string wound $Q_1 ...
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What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
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SUSY Multiplets

Why is it that in vector supermultiplets, the left and right chiral components of the gauginos must transform in the same representations of all gauge groups, i.e a chiral theory for such fermions is ...
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On the action of superconformal generators in maximally supersymmetric Yang-Mills

Consider maximally supersymmetric Yang-Mills theory in 3+1 dimensions. This theory has 32 supercharges: 16 ordinary ones, conventionally labeled $Q$; and 16 superconformal ones, conventionally ...
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51 views

Boson in Superstring

I'm confused about a point. Superstring sigma model is $$ S=-\frac{T}{2}\int\mathrm{d}^2z \left[\eta^{ab}\partial_aX^\mu\partial_b X_\mu -i\bar\psi^\mu\rho^a\partial_a\psi_\mu \right], $$ of course, ...
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29 views

Gauge mediated SUSY breaking

I have seen it claimed that in SUSY gauge mediated breaking there can be no flavour changing terms because the mediation is flavour blind. What does this mean and how does it work?
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68 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
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D-branes conserving only half of the supersymmetries

Concerning D-branes as BPS states from T-duality. In D-Branes by Johnson (and other sources) I find the following statement (p.196): "Only the total [supersymmetric] charge of $Q_a+\tilde{Q}_a$ of ...
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Has anyone studied anomalous supersymmetry?

In this paper (and others), the authors study a supersymmetric model where the supercharge suffers an ABJ anomaly. Has anyone studied a supersymmetry with a 't Hooft anomaly (gauging the ...
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$\mathcal{N} = 4$ Super-Yang Mills propagators

In $\mathcal{N} = 4$ Super-Yang mills there are only massless particles. If one wishes to obtain a heavy quark one can see the SYM theory as a stack of (N+1)-branes in AdS$_5 \times$S$^5$ where one ...
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Fermion Trucation

I recently posted about truncating fermions in supergravity Lagrangians and got a good answer about how this gives a vev to the bosonic content and therefore freezes it to a stationary point of the ...
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Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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D4 branes ending on NS5 branes (Witten's construction): query about harmonic functions

This query stems from Witten's paper, ''Solutions of Four-Dimensional Field Theories via M Theory'' (hep-th/9703166). Specifically, consider Type IIA string theory, and suppose one has a stack of NS5 ...
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Number of supercharges in $N\ge 1$ SUSY in $d\ge4$ dimensions

I have a couple of questions concerning supercharges and superalgebras: 1, In four-dimensions, the minimal spinor representations are Weyl spinors. These have 4 real degrees of freedom (dof). This ...
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72 views

Ignoring fermions in string theory/supergravity

Often in string theory/supergravity, papers will say something along the lines of "we set all the fermions to zero and focus purely on the bosonic field content". See e.g. the final lines on p3 of hep-...
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What is the role of chiral compensator?

When studying SUGRA inflation, I stumbled upon a notion of "chiral compensator". What is its role? I don't remember seeing it in Wess & Bagger textbook.
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Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
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Nonperturbative corrections that can break SUSY

I am puzzled by a statement that is made regarding non-perturbative corrections breaking supersymmetry. Specifically, consider a one-dimensional system, described by the Hamiltonian $$H = \frac{1}{2}...
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Why must SUSY be broken in SUGRA inflation?

Why must supersymmetry be broken during the inflation in supergravity models? How does adding supersymmetry to power-law or Starobinsky models spoil inflation? And is breaking of SUSY needed for ...
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$R$-Symmetry Group

On p238/239 of the Freedman and van Proeyen book on Supergravity, they show how the $R$-symmetry group must be $U(\mathcal{N})$ for $\mathcal{N}$-extended supersymmetry in $d=4$. At the bottom of ...
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Tranformation of a spinor in the self representation and conjugate representation of $SL(2,\mathbb{C})$

The transformation rules for a spinors as per Introduction to Supersymmetry by Wiedamann on Pg.38 is be summarized as: $$\begin{align} \psi_{\alpha} \mapsto \psi'_{\alpha} &= M_{\alpha}^{\beta}...
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What do different supercharges corrrespond to? Is creation mathematically close to fock space?

We may have $I =1,2,..N$ where it is said that this corresponds to $N$ supercharges, $Q^I$. By the supersymmetry algebra, $$[M_{\mu\nu},{\overline{Q}}^{I\dot{\alpha}}] = i(\sigma_{\mu\nu}){^{\dot{\...
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Coleman Mandula theorem and translations

I don't know what Coleman Mandula theorem is, however if I were forced to say something about it, I will say it is a statement that suggests that internal and spatial symmetries have no unique ...
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Physical meaning of the Morse functions? [closed]

What is the physical correspondence of the Morse functions in a physical system? Currently I am studying Mirror symmetry but I can not get a physical intuition out of it.
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Supertrace of holonomy of commutator

On page 47 of Surface operators in four-dimensional topological gauge theory and Langlands duality by Kapustin et al., the following expression is given \begin{equation} \delta\mathcal{N}=d(\omega_\...
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Femionic vacuum expectation value

To have maximally symmetric space-time (Minkowski, dS and AdS), why should we have zero vacuum expectation value for fermionic fields?
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How do I obtain the SUSY Transformations from Poisson Brackets?

In Friedman's and Van Proyen's Supergravity textbook it is explained how one can get the supersymmetry transformations using the conserved currents. Specifically this is in section 6 where we are ...