Yes, there's a correlation and a causation. Here are 9 studies that prove it:
The present work suggests that self-control relies on glucose as a limited energy source. Laboratory tests
of self-control (i.e., the Stroop task, thought suppression, emotion regulation, attention control) and of
social behaviors (i.e., helping behavior, coping with thoughts of death, stifling prejudice during an
interracial interaction) showed that (a) acts of self-control reduced blood glucose levels, (b) low levels
of blood glucose after an initial self-control task predicted poor performance on a subsequent self-control
task, and (c) initial acts of self-control impaired performance on subsequent self-control tasks, but
consuming a glucose drink eliminated these impairments. Self-control requires a certain amount of
glucose to operate unimpaired. A single act of self-control causes glucose to drop below optimal levels,
thereby impairing subsequent attempts at self-control.
—Self-Control Relies on Glucose as a Limited Energy Source: Willpower Is
More Than a Metaphor by Gailliot, et al., Journal of Pers and Soc Psycholy (2007), Vol. 92, No. 2, 325–336, DOI: 10.1037/0022-35184.108.40.2065
Past research indicates that self-control relies on some sort of limited energy source. This review suggests that blood glucose is one important part of the energy source of self-control.
—Unlocking the Energy Dynamics of Executive Functioning: Linking Executive Functioning to Brain Glycogen doi: 10.1111/j.1745-6924.2008.00077.x -
Persp on Psychol Sc, July 2008 vol. 3 no. 4 245-263
This provides a different spin on it:
The strength model suggests that self-control relies on a limited resource. One candidate for this resource is glucose. Counter to the proposals of the glucose hypothesis, this study argues that the resource issue is one of allocation, not of limited supply.
—The Role of Glucose in Self-Control: Another Look at the Evidence and an Alternative Conceptualization - Pers Soc Psychol Rev May 1, 2012 16: 143-153
Interpersonal provocation is a common and robust antecedent to aggression. Four studies identified angry rumination and reduced self-control as mechanisms underlying the provocation—aggression relationship. Following provocation, participants demonstrated decreased self-control on an unpleasant task relative to a control condition (Study 1). When provoked, rumination reduced self-control and increased aggression. This effect was mediated by reduced self-control capacity (Study 2). State rumination following provocation, but not anger per se, mediated the effect of trait rumination on aggression (Study 3). Bolstering self-regulatory resources by consuming a glucose beverage improved performance on a measure of inhibitory control following rumination (Study 4). These findings suggest that rumination following an anger-inducing provocation reduces self-control and increases aggression. Bolstering self-regulatory resources may reduce this adverse effect.
—Understanding Impulsive Aggression: Angry Rumination and Reduced Self-Control Capacity Are Mechanisms Underlying the Provocation-Aggression Relationship -
Pers Soc Psychol Bull June 1, 2011 37: 850-862
Worthy of the Annals of Improbable Research:
We test the
common caricature of realism that justice is “what the judge ate
for breakfast” in sequential parole decisions made by experienced
judges. We record the judges’two daily food breaks, which result in
segmenting the deliberations of the day into three distinct “decision sessions.” We ﬁnd that the percentage of favorable rulings
drops gradually from ≈65% to nearly zero within each decision
session and returns abruptly to ≈65% after a break. Our ﬁndings
suggest that judicial rulings can be swayed by extraneous variables
that should have no bearing on legal decisions.
—Extraneous factors in judicial decisions -
Proc. Natl. Acad. Sci. USA April 26, 2011 108: 6889-6892
These researchers prove reality is not so simple, after all:
Much recent research suggests that willpower—the capacity to exert self-control—is a limited resource that is depleted after
exertion. We propose that whether depletion takes place or not depends on a person’s belief about whether willpower is
a limited resource. Study 1 found that individual differences in lay theories about willpower moderate ego-depletion effects.
—Ego Depletion--Is It All in Your Head?: Implicit Theories About Willpower Affect Self-Regulation -
Psychological Science November 1, 2010 21: 1686-1693
A group of participants who drank a soft drink that contained sugar showed a reduced rate of future discounting afterward, when we controlled for sex, age, body mass index, and the taste of the drink. In contrast, a group of participants who drank a soft drink that contained artificial sweetener showed an increased rate of future discounting. Blood glucose levels not only varied as a result of caloric intake but also regulated the rate of future discounting, according to participants’ dynamic body-energy budget.
—Sweet Future: Fluctuating Blood Glucose Levels Affect Future Discounting -
Psychological Science February 1, 2010 21: 183-188
Past work suggests that executive functioning relies on glucose as a depletable energy, such that executive functioning uses a relatively large amount of glucose and is impaired when glucose is low. Glucose from the bloodstream is one energy source for the brain, and glucose stored in the brain as glycogen is another. A review of the literature on glycogen suggests that executive functioning uses it in much the same way as glucose, such that executive functioning uses glycogen and is impaired when glycogen is low. Findings on stress, physical persistence, glucose tolerance, diabetes, sleep, heat, and other topics provide general support for this view.
—Unlocking the Energy Dynamics of Executive Functioning: Linking Executive Functioning to Brain Glycogen -
Perspectives on Psychological Science July 1, 2008 3: 245-263
This experiment used the attraction effect to
test the hypothesis that ingestion of sugar can reduce reliance on intuitive, heuristic-based decision making. In the
attraction effect, a difﬁcult choice between two options is
swayed by the presence of a seemingly irrelevant ‘‘decoy’’
option. We replicated this effect and the ﬁnding that the
effect increases when people have depleted their mental
resources performing a previous self-control task.
—Toward a Physiology of Dual-Process Reasoning and Judgment: Lemonade, Willpower, and Expensive Rule-Based Analysis - Psychological Science March 1, 2008 19: 255-260