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

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contraction of the spinor F with a conjugate spino $\bar{\epsilon}$ is bosonic?

In this Why $\delta F = B\epsilon$ and not $F=B \epsilon$ in supersymmetry?, I asked ACuriousMind why would one epsilon be without a bar and the other with a bar here: $$\delta F = B\epsilon, \tag{1} ...
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74 views

Fayet-Iliopoulos terms

It is mentioned in first page of this paper by Seiberg and Komargodski that the Lagrangian in superspace of a $U(1)$ gauge SUSY theory with FI terms is not gauge invariant. However, the FI terms in ...
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66 views

State counting in the d = 1+2, $\cal{N} = 2$ vector multiplet

The question is from Box 8.2, page 282 of the book "Gauge Gravity Duality" by Ammon and Erdmenger. The link to the specific page from Google Books is here. According to the authors, a $\mathcal{N} = ...
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How does one determine the genus of the ultraviolet curve from Seiberg-Witten curve?

In Gaiotto's construction of 4d ${\cal N}=2$ theories, one starts with 6d (2,0) theory and compactify it on the Riemann surface, which is called the ultraviolet curve of the ${\cal N}=2$ theory. In ...
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18 views

Supersymmetric variation of $F$ term using super Jacobi identity [closed]

Basically, i am solving problems in note with a slightly different notation. \begin{align} [Q_\alpha F] = -i \lambda_\alpha (x), \quad [ \bar{Q}_{\dot{\alpha}},F] = -i \bar{\chi}_{\dot{\alpha}} ...
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98 views

Supercovariant Derivative action

My query is with Weinberg Vol3 equation just above 26.7.22 Weinberg follows Majorana Superfield formalism. Where, covariant derivative is defined as, $$D_{R\alpha}=-\epsilon_{\alpha ...
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72 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
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59 views

Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
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48 views

Lorentz group in SUSY

Why do we carry Lorentz group to be included also in supersymmetry? That is after we extend our symmetry to supersymmetry, we carry with us the Lorentz group. Why not other group instead?
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Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and ...
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237 views

Learning about super-symmetric quantum mechanics and integrable systems

I'm an undergraduate interested in theory. I recently asked one of my professors, a physicist in the particle theory group at my school, if he'd be willing to take on an undergraduate for a senior ...
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On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
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39 views

Why are only certain fluxes allowed in 11D SUGRA?

In Type IIA/IIB string theory we can have various fluxes, such as the 3-form H-flux, and the various Ramond-Ramond fluxes in even/odd dimensions. In 11D SUGRA, however, the field content seems to ...
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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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83 views

Projective superspace: why extra bosonic coordinates

I'm studying the projective superspace formalism for N = 4 supersymmetric $\sigma$-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action? I ...
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1answer
83 views

Killing vector and one-form [closed]

p. 21 in this paper (http://arxiv.org/abs/0704.0247) $V$ is Killing vector, where $V^2 = −4b\bar{b}$, which means it is timelike Killing vector. The authors say: From $V^2 = −4|b|^2$ and $V = ...
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What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

When reading about Higgs and Coulomb 'phases' I came across two separate definitions: The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field ...
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61 views

How do we know if a Killing Spinor is Time-like or Null?

How to know whether a Killing spinor orbit is time-like or null? This is present in a paper like this 29/39 here. I'm not asking for a technical answer, just a logical cliche answer chit-chat answer. ...
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32 views

Basic Dirac Spinors question

Here p. 25, it says Generically, the space of Dirac spinors has $2^{d/2}$ (complex) components, and one can recast them in terms of the complexified space of forms on $\mathbb{R}^{d/2}$. My ...
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99 views

What are susy transformations for N=2 sugra?

Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories. As suggested by some books and papers on ...
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72 views

What does $δF=0$ imply?

Please have a look here section 12.6. It says here that Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations of motion. It is ...
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148 views

Why supergravity is extension of GR?

Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special ...
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122 views

I do not understand this comparison?

It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion. I do not understand this discussion though. Specifically, ...
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65 views

Superpotential for Gaussian potential well? [closed]

so I am looking for the super potential of a Gaussian well, namely $V= -e^{-x^2/2}$, and the super potential has to satisfy the Riccati equation,$ − W′ ( x ) + W ( x ) = V ( x ) − a$. Somehow I ...
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64 views

Which are some best books to learn supersymmetry?

I am interested in a book that is mathematically precise. I am not expecting a mathematicians book like the one by Deligne.
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51 views

Electro-mangetic duality, Quantum electro dynamics and N=4 SYM

This question is extension of Electro magnetic duality, Strong weak duality and N=4 super Yangmils which i asked before. Here what i want to know is compare of QED and N=4 SYM in terms of ...
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47 views

Nahm's theorem and related with SYM ;other theories

To study $S$-duality in more detail, i tried to read, Electric-magnetic duality and the Geometric Langlands Program. In section 2.1, there is a comment about 10d SYM. Excerpt from the paper above, ...
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62 views

Electro magnetic duality, Strong weak duality and N=4 super Yangmils

How we can interpret this self-dual, or duality in terms of generalized version of electro magneitc duality, or Strong weak duality. Let me address some basic information. First, electro magnetic ...
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55 views

How would superpartners explain dark matter? (Supersymmetry)

This is probably very basic but I can't quite find the answer in other questions. As I understand it we are hoping to create supersymmetric particles at the LHC (in this second run) and these ...
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Are SUSY transformations free from anomalies?

Although I've studied supersymmetic field theories for several years, there is a fundamental problem annoying me: Do SUSY transformations (including both the ordinary ones in various dimensions and ...
3
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78 views

Supersymmetry as a solution of hierarchy problem

Hierarchy problem is the statement of why the weak force is much stronger than gravity. In terms of coupling constant, weak force (Fermi coupling) is much larger than gravity (Newton's constant). I ...
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62 views

Seiberg duality and IR fixed point

This question is related with Seiberg duality for $SU(N)$ gauge theory which states a duality between electric theory, $SU(N_c)$ gauge theory with $N_f$ flavors is dual to its magnetic theory, ...
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How can we use Majorana spinors for charged fermions in MSSM?

According to "Supersymmetry in Particle Physics" by Ian Aitchison (see e.g. p62 of arXiv), in the Minimal Supersymmetric Standard Model (MSSM) we can use Majorana language to build supermultiplets: ...
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Is a $SU(2)$ supergauge theory really a $SU(2)$ gauge theory?

Consider $SU(2)$ supergauge theory with $A$, a doublet of two chiral superfields in the fundamental representation. $$A= \begin{pmatrix} \Phi_1\\ \Phi_2 \end{pmatrix}$$ where $\Phi_1$ and $\Phi_2$ ...
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48 views

Superpotential Symmetry

Superpotential in general has the form $W=a_n\Phi^n$. If I require that my superpotential should be invariant under the following global transformation, $\delta \Phi=i\epsilon \Phi$ and $\delta ...
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What exactly is the “diagonal embedding” in the supersymmetric topological twist?

Consider $\mathcal{N}=2$ pure SYM theory. If we want to put the theory in a 4-manifold we take its topological twist. The global symmetry group $$G= SU(2)_{+} \times SU(2)_{-} \times SU(2)_I \times ...
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2answers
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ΧΕΝΟΝ1Τ: Will it fail to discover DM? Why is it necessary? What benefits for society?

Since a new experiment (ΧΕΝΟΝ1Τ) will take place in Italy to directly detect WIMPs and since there are already many experiments trying to do the same or something similar (e.g. CERN LHC, LUX, CoGent, ...
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65 views

Matching bosonic and fermionic degrees of freedom in Wess-Zumino Lagrangian

In Wess-Zumino model, supersymmetric Lagrangian in addition to the ordinary complex scalar field $\phi$ contains auxiliary field $F$ (also complex scalar) to match the degrees of freedom of the Weyl ...
3
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218 views

Supersymmetric Sigma Model

I was working through the Mirror Symmetry book by Clay Math Institute. It deals with supersymmetric sigma model in 10.4 section. It doesn't derive how the action is invariant under the variation. I am ...
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Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
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What does it mean for an action to be defined “on-shell”?

Some actions like 11D supergravity are defined "on-shell". What does this mean exactly? Can you give me an example? Say for example the Klein-Gordon action. Can this be defined on-shell too?
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Construction of $\mathcal O(-1) \oplus \mathcal O(-1)$ over $CP^1$ [closed]

First, Consider a $\phi$ as a coordinates on a copy of $Z= C^N$ Then, I know \begin{align} |\phi_1|^2 + |\phi_2|^2 + \cdots |\phi_N|^2 = r \end{align} which describe $S^{2N-1}$. Implementing $U(1)$ ...
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36 views

Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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Jim Gates' discovery of error-correcting codes in equations of supersymmetry

Can anyone explain what's going on here, in a way that isn't just a lot of gee-whiz? Here's the arXiv article. I'm more of a computer science person than a physicist, so error-correcting codes are ...
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Chiral multiplet : Fundamental and adjoint representation and its Lagrangian

In supersymmetry theory, consider $4d$ $N=1$ theory, we know that chiral superfield (In fundamental representation $\Phi \rightarrow e^{i\alpha} \Phi$) $\Phi$ and its lagrangian is given as ...
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Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
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Intuition behind Nekreasov's instanton partition function. What do the partitions represent exactly?

I am struggling to understand many things behind Nekrasov's solution. Firstly I want to understand the following In this theory, $a$ represents VEVs the Higgs scalar. So, is the gauge field of the ...
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M-theory compactified on $S^4$

I am trying to understand what happens to the 32 supersymmetries of M-theory when it is compactified on $S^4$, with the other seven dimensions being flat, e.g., $\mathbb{R^7}$, $\mathbb{R^6} \times ...
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How can we reduce the number of necessary parameter to 19 in phenomenological Minimal Supersymmetric Standard Model (pMSSM)?

I am very new in SUSY and I heard something about pMSSM. Question is that how we can reduce the number of necessary parameter to 19 in pMSSM. If you have any suggestion as a brief introduction or any ...